• Present 2018

#### Research Scientist

CSIRO, Data61

• Present 2014

#### Research Fellow

The University of Melbourne, Melbourne School of Engineering

• 2014 2010

#### Research Assistant

KTH Royal Institute of Technology, Automatic Control Department

• 2013

#### Visiting Student Researcher

The University of California at Berkeley, Department of Electrical Engineering and Computer Sciences

### Education

• Ph.D. 2014

Ph.D. in Automatic Control

KTH Royal Institute of Technology

• M.Sc.2010

M.Sc. in Electrical Engineering (Control Engineering)

Sharif University of Technology

• B.Sc.2008

B.Sc. in Electrical Engineering (Control Engineering)

Sharif University of Technology

### Honors, Awards, and Grants

• 2018
DSTG (Defence Science and Technology Group)
Funding for ‘DPAIP, Data Privacy in AI Platforms: Risks Quantification and Defence Apparatus’ with Prof. Dali Kaafar and Dr. Hassan Asghar at Macquarie University, Dr. Paul Tyler at Data61, and Prof. Yang Xiang at Swinburne University of Technology.
• 2017
VESKI Fellowship
A prestigious award of up to $18,000 to undertake a short-term overseas study mission to assist in career development not available in Australia. • 2016 DSTG (Defence Science and Technology Group) Dr. Shames, Dr. Rubinstein, and I were awarded AU$93,097 from DSTG (Defence Science and Technology Group) in addition to 3 ground robots.
• 2016
McKenzie Fellowship
I was awarded the McKenzie Postdoctoral Fellowship by the University of Melbourne (3 years salary plus AU$25,000 project funding). • 2015 Early Career Researcher Grant I was awarded AU$33,696 Early Career Researcher Grant from the University of Melbourne (declined due to conflict with McKenzie Postdoctoral Fellowship).
• 2015
Finalist in the 2015 EECI Phd Award
I was the finalist in the 2015 European Embedded Control Institute (EECI) PhD Award (one of 4 PhD graduates from across Europe in the field of Control for Complex and Heterogeneous Systems).
• 2015
Wallenberg Foundation Postdoctoral Scholarship Program
I was awarded US$100,000 from the Wallenberg Foundation Postdoctoral Scholarship Program at Stanford University (declined due to previous commitments). • 2015 IEEE Control System Society Outreach Fund I was awarded US$5,750 (as the project leader) for "Control Engineering for High School Students and Teachers: An Online Platform Development" form IEEE Control System Society Outreach Fund.
• 2014
Outstanding Reviewer, IEEE Transactions on Control of Network Systems
I was awarded outstanding reviewer of IEEE Transactions on Control of Network Systems in 2014.
• 2013
Travel Grant from Sten och Lisa Velanders Forskningsfond
I was awarded travel grant by Sten och Lisa Velanders Forskningsfond to attend the 52nd IEEE Conference on Decision and Control (CDC 2013), Florence, Italy.
• 2012
Best Presentation in Session at ACC 2012
I was awarded best presentation in session at American Control Conference (ACC 2012), June 27-29, 2012, Montreal, Canada.
• 2011
Travel Grant for EECI-HYCON2 Graduate School
I was awarded travel grant to attend the course on Specification, Design and Verification of Distributed Embedded Systems'' at EECI-HYCON2 Graduate School on Control 2011.
• 2010
Ranked First between M.Sc. Students in Control Engineering
I was ranked 1st among 15 M.Sc. students in Control Engineering, School of Electrical Engineering, Sharif University of Technology, Tehran, Iran
• 2010
I was given an honorary admission for graduate studies in Control Engineering, School of Electrical Engineering, Sharif University of Technology, Tehran, Iran.
• 2008
Ranked First between B.Sc. Students in Control Engineering
I was ranked 1st among 40 B.Sc. students in Control Engineering, School of Electrical Engineering, Sharif University of Technology, Tehran, Iran.
• 2005
Ranked 19th (among more than 400,000 participants) in the Nationwide University Entrance Exam
I was ranked 19th among more than 400,000 participants in the nationwide university entrance exam for B.Sc. degree in Iran.
• 2004
Silver medal at national Physics Olympiad
I recieved a silver medal at 17th national Physics Olympiad in Iran.

• ### Effects of Privacy and Strategic Behavior in Crowd-Sensing

We quantitatively study issues pertaining to privacy in communication between the crowd and service providers.

With a yearly expansion rate of 30% for mobile broadband subscriptions and smartphones accounting for 65-70% of all the sold mobile phones, we are truly living in a connected world. This constant state of connectedness presents many opportunities to increase productivity through the potential avenues it affords for data collection and influencing the environment. The aim of this project is to investigate aspects of using such technologies to leverage crowd sourcing in the monitoring and estimation of large-scale systems and to understand the implications of privacy in this setup. The project draws on tools from mathematical systems theory, game theory, information theory, and signal processing.

Networked devices can act as sensing units that provide the data used to estimate a variable of interest. The variable of interest could be the traffic (Waze), mobile coverage (Sensorly), quality of service or product (Amazon), water levels in transport and drainage canals (Mobile Water Management), household power consumption (smart electricity meters), or mobility demand surveys (Freeway Management System). The devices could be directly controlled by human users, e.g. smart phones. On the other hand, they could be passive stationary sensors that collect public information, e.g. highway vehicle counters, or private information, e.g. smart meters. Third-party systems for sensing will become more relevant as we move towards smart cities in which individual devices communicate with infrastructure for the provision of services and to ensure efficient and safe operation. In view of these possibilities, networked devices can be abstractly modelled as agents with different requirements, behaviours, and capabilities that can coexist in an environment. For example, privacy might be a very important factor for a human agent, while it is a non-issue for a stationary sensor collecting data in a public space. Different sensors might provide measurements with different accuracy levels based on their power consumption profile. Further, smartphones can be hacked to feed false measurements to a sensing scheme. Individual participants might also want to change the outcome for their benefit. Therefore, robust mechanisms are needed for estimation and control when crowd-sourcing of sensor functions.

• ### Security Analysis of Smart Grids: A Cyberphsyical Systems Approach

We aim to study the scenarios where an adversarial agent's objective is to compromise a cyberphysical system via sophisticated attacks.

Critical infrastructure, such as electricity grids, water distribution networks, and transport systems, are examples of cyber-physical systems. Among these systems, the energy and power assets are of significant importance as they underpin all facets of modern life (e.g. food, health, manufacturing, commerce and trade, etc). These systems consist of large-scale physical processes monitored and controlled by networked control systems running over a heterogeneous set of communication and computers networks. Although the use of such powerful information technology (IT) systems adds flexibility and scalability, it also increases the vulnerability to hackers and other malicious entities capable of cyber attacks.

In this project, we aim to study the scenarios where an adversarial agent's objective is to compromise a cyberphysical system via sophisticated attacks. Specifically, we want to (1) develop an optimization framework that facilitates studying the effect of attacks on the outputs and states of a cyberphysical system, (2) identify optimal attack strategies with the highest impact on the network, (3) investigate the effect of interference with the optimization algorithms that are used to solve the economic dispatch problems, and (4) study the vulnerability of a power network to sudden injection (or draining) of power.

• ### Optimal Contract Design for Information Acquisition and Sensing

We design optimal contracts from the perspective of the budget required for accurate information acquisition and sensing.

The behaviour of third-party strategic sensors, specifically the effort expended to collect measurements in response to incentives, are modelled in terms of a contract game which is exploited in a simple averaging estimation scheme. Conditions for the existence and the uniqueness of the corresponding equilibrium are presented. The equilibrium is constructed explicitly and its properties in response to the incentives are studied. Following this, optimal contracts are designed from the perspective of the budget required for accurate information acquisition and sensing.

• ### Distributed Implementation of VCG Mechanisms

We propose pricing mechanisms that incentivise agents to faithfully implement the distributed algorithms.

Recently, we started looking at large scale resource allocation problems for multiple agents, and a situation in which agents are suggested to take part in distributed optimization algorithms such as, dual decomposition, to solve the problem. Here, we assumed that the agents are strategic, that is, they want to minimize their own individual cost rather than the global social cost. Therefore, if we do not carefully design a taxing mechanism, these agents are not going to solve the original problem that we were considering. Now, inspired by the classical Vickrey-Clarke-Groves mechanism and more recent algorithmic mechanism design theory, we proposed a tax mechanism that incentivises agents to faithfully implement the intended algorithm. To do so, we defined a new notion of asymptotic incentive compatibility to characterize a desirable property of the proposed class of mechanisms, which provides a sequence of mechanisms that gives agents a diminishing incentive to deviate from suggested algorithm.

• ### Decentralized Control Design with Limited Plant Model Information

We investigate the trade-off between the amount of model information exploited by a control design strategy and the best possible closed-loop performance.

Large-scale control systems are often composed of several smaller interconnected units. For these systems, it is common to employ local controllers, which observe and act locally. At the heart of common control design procedures for distributed systems lies the often implicit assumption that the designer has access to the global plant model information when designing a local controller. However, there are several reasons why such plant model information would not be globally known. One reason could be that the designer wants the parameters of each local controller to only depend on local model information, so that the controllers are not modified if the model parameters of a particular subsystem change. It might also be the case that the design of each local controller is done by individual designers with no access to the global plant model, for instance, due to the fact that the designers refuse to share their model information since they consider it private. In this research problem, we investigate the trade-off between the amount of model information exploited by a control design strategy and the best possible closed-loop performance.

• ### Transportation Networks

We are interested in designing controllers that can increase the chance of heavy-duty vehicle platooning to improve the fuel efficiency on the road and reduce the carbon emissions.

We consider heterogeneous routing and congestion games, where each driver or vehicle belong to a certain type. The type determines the cost of traveling along an edge as function of the flow of all types of drivers or vehicles over that edge. Our interest in solving this problem is motivated by traffic networks in which the assumption that the drivers are of the same type might not be very realistic. For instance, due to fuel consumption, heavy-duty vehicles and cars might experience different costs for using the road even if their travel times are equal. We started examining this phenomenon in congestion games where the heavy-duty vehicles observe an increased efficiency when a higher number of heavy-duty vehicles are present on the same road as them (because of a higher platooning possibility and, therefore, an improved fuel efficiency) while this may not true for cars.

### Filter by type:

#### [J29] Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

Carlos Murguia, F. Farokhi, and Iman Shames
Journal Papers Submitted.

#### [J28] Development and Analysis of Deterministic Privacy-Preserving Policies Using Non-Stochastic Information Theory

F. Farokhi
Journal Papers Submitted.

#### [J27] Optimal Stochastic Evasive Maneuvers Using the Schrodinger’s Equation

F. Farokhi and M. Egerstedt
Journal Papers Submitted.

#### [J26] Privacy-Preserving Public Release of Datasets for Optimization-Based Machine Learning

F. Farokhi
Journal Papers Submitted.

#### [J25] Secure Networked Control Systems Design Using Semi-Homomorphic Encryption

Y. Lin,F. Farokhi, I. Shames, D. Nesic
Journal Papers Submitted.

#### Abstract

A secure nonlinear networked control systems (NCSs) design using semi-homomorphic encryption, particularly, Pailier encryption is studied. Under certain assumptions, control signal computation using encrypted signal directly is possible under a semi-homomorphic encryption scheme. Thus, the security of the NCSs is further enhanced by concealing information on the controller side. On the other hand, in traditional encryption techniques, encrypted signals are decrypted before control computation and are encrypted again after computation for transmission. While this is highly desirable from privacy point of view, additional technical diculties in the design and analysis of NCSs are induced compared to standard NCSs. In this paper, we provide sufficient conditions on the encryption parameters that guarantee stability of the NCS, and show a trade-off between the required computational resources and the closed loop performance when there are disturbances. The proof technique is based on Lyapunov methods.

#### [J24] Security Analysis of Quantized Bayesian Estimators

D. D. Selvaratnam, F. Farokhi, and I. Shames
Journal Papers Submitted.

#### Abstract

Security of networked Bayesian source localisation algorithms is analysed in this paper. The Bayesian estimators construct the probability density function of the location of the source from quantised measurements. Understanding fundamental limits in the performance of an adversary for manipulating the posterior of the Bayesian estimator is the main focus of the paper. The analysis is performed for cases where the estimator is not aware of the presence of the adversary, as well as the case where the estimator is aware of the attacker.

#### [J23] Private Ride Sharing and Routing Using Semi-Homomorphic Encryption

F. Farokhi, I. Shames, and K. H. Johansson
Journal Papers Submitted.

#### Abstract

A secure and private framework for communication between two agents is developed. An agent can ask questions or submit queries regarding the interest of the other agents about using a road at a specific time of the day in an encrypted fashion. The framework is developed with the aid of semi-homomorphic encryption (namely, the Paillier’s encryption method), which allows algebraic manipulation of plain data without the need of decryption using appropriate computations over encrypted data. Strong privacy and security guarantees are proved for the agents. Subsequently, the aforementioned semi-homomorphic encryption is utilized to develop a privacy-aware routing algorithm.

#### [J22] Feedback Control Using a Strategic Sensor

F. Farokhi
Journal Papers Submitted.

#### Abstract

A dynamic estimation and control problem with a strategic sensor is considered. The strategic sensor may provide corrupted messages about the state measurements of a discrete-time linear time-invariant dynamical system to the system operator (or the controller). The system operator then uses this information to construct an estimate of the state of the system (and perhaps private variables of the sensor). The estimate is used to control the system to achieve the operator's desired objective. The problem is formulated as a game, which might be conflicting to that of the strategic sensor. An equilibrium of the game is computed and its properties are investigated.

#### [J21] Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information

F. Farokhi and Henrik Sandberg
Journal Papers Submitted.

#### Abstract

The problem of preserving the privacy of individual entries of a database with constrained additive noise is considered. Anyone, including an adversary, can submit linear or nonlinear queries to a server possessing the private database. The server returns a response to the query that is systematically corrupted with an additive random noise whose support is a subset or equal to a pre-defined constraint set. The Cramer-Rao bound is used to relate the variance of the estimation error of any unbiased estimators of the database (which may be used by the adversary) to the trace of the inverse of the Fisher information matrix. A measure of privacy using the Fisher information matrix is developed. The probability density that minimizes the Fisher information (as a proxy for maximizing the measure of privacy) is computed. An extension to dynamic problems is finally presented.

#### [J20] Optimal Contract Design for Effort-Averse Sensors

F. Farokhi, I. Shames, and M. Cantoni
Journal Papers International Journal of Control, In Press.

#### Abstract

Consider a group of effort-averse, or lazy, sensors that seek to minimize the effort invested to collect measurements of a variable. Increasing the effort invested by the sensors improves the quality of the measurements provided to the central planner but this incurs increased costs to the sensors. The central planner, which processes the sensor measurements, employs an averaging estimator. It also determines contracts for rewarding sensors based on the measurements obtained. The problem of designing a contract that yields an estimation-error based quality-of-service level in return for the reward extended to sensors is investigated in this paper. To this end, a game is formulated between the central planner and the sensors. Conditions for the existence and uniqueness of an equilibrium are identified. The equilibrium is constructed explicitly and its properties in response to a reward based contract are studied. It turns out that the central planner, while not being able to directly measure the effort invested by the sensors, can enhance the estimation quality by rewarding each sensor based on the distance of its measurements from the output of the averaging estimator. Ultimately, optimal contracts are designed from the perspective of the budget required for achieving a specified level of estimation error.

#### [J19] Scalable Computation for Optimal Control of Cascade Systems with Constraints

M. Cantoni, F. Farokhi, E. Kerrigan, and I. Shames
Journal Papers International Journal of Control, In Press.

#### Abstract

A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure of performance, are all separable with respect to the spatial dimension of the underlying cascade of sub-systems, as well as the temporal dimension of the dynamics. By virtue of this structure, the computation cost of an interior-point method for an equivalent quadratic programming formulation of the optimal control problem can be made to scale linearly with the number of sub-systems. However, the complexity of this approach grows cubically with the time horizon. As such, computational advantage becomes apparent in situations where the number of sub-systems is relatively large. In any case, the method is amenable to distributed computation with low communication overhead and only immediate upstream neighbour sharing of partial model data among processing agents. An example is presented to illustrate an application of the main results to model data for the cascade dynamics of an automated irrigation channel.

#### [J18] Fisher Information as a Measure of Privacy: Preserving Privacy of Households with Smart Meters Using Batteries

F. Farokhi and H. Sandberg
Journal Papers IEEE Transactions on Smart Grid, In Press.

#### Abstract

In this paper, batteries are used to preserve the privacy of households with smart meters. It is commonly understood that data from smart meters can be used by adversaries to infringe on the privacy of the households, e.g., figuring out the individual appliances that are being used or the level of the occupancy of the house. The Cramér-Rao bound is used to relate the variance of the estimation error of any unbiased estimator of the household consumption from the aggregate consumption (i.e., the household plus the battery) to the Fisher information. Subsequently, optimal policies for charging and utilizing batteries are devised to minimize the Fisher information (in the scalar case and the trace of the Fisher information matrix in the multi-variable case) as a proxy for maximizing the variance of the estimation error of the electricity consumption by adversaries (irrespective of their estimation policies). The policies are chosen to respect the physical constraints of the battery regarding capacity, initial charge, and rate constraints. The results are demonstrated on real power measurement data with non-intrusive load monitoring algorithms.

#### [J17] Integration of Information Patterns in the Modeling and Design of Mobility Management Services

A. Keimer, N. Laurent-Brouty, F. Farokhi, H. Signargout, V. Cvetkovic, A. M. Bayen, K. H. Johansson
Journal Papers Proceedings of the IEEE, 106 (4), pp. 554-576, 2018.

#### Abstract

Over the last decade, the rise of the mobile internet and the usage of mobile devices has enabled ubiquitous traffic information. With the increased adoption of specific smartphone applications, the number of users of routing applications has become large enough to disrupt traffic flow patterns in a significant manner. Similarly, but at a slightly slower pace, novel services for freight transportation and city logistics improve the efficiency of goods transportation and change the use of road infrastructure. The present article provides a general four-layer framework for modeling these new trends. The main motivation behind the development is to provide a unifying formal system description that can at the same time encompass system physics (flow and motion of vehicles) as well as coordination strategies under various information and cooperation structures. To showcase the framework, we apply it to the specific challenge of modeling and analyzing the integration of routing applications in today's transportation systems. In this framework, at the lowest layer (flow dynamics) we distinguish app users from non-app users. A distributed parameter model based on a non-local partial differential equation is introduced and analyzed. The second layer incorporates connected services (e.g., routing) and other applications used to optimize the local performance of the system. As inputs to those applications, we propose a third layer introducing the incentive design and global objectives, which are typically varying over the day depending on road and weather conditions, external events etc. The high-level planning is handled on the fourth layer taking social long-term objectives into account.

#### [J16] Towards Encrypted MPC for Linear Constrained Systems

M. Schulze Darup, A. Redder, I. Shames, F. Farokhi, and D. E. Quevedo
Journal Papers IEEE Control Systems Letters, 2(2), pp. 195-200, 2018.

#### Abstract

We present an encrypted model predictive control (MPC) scheme for linear constrained systems. More precisely, we show that homomorphic encryption can be used to realize a secure and private cloud-based evaluation of an MPC if the corresponding piecewise affine control law is explicitly given.

#### [J15] Secure and private control using semi-homomorphic encryption

F. Farokhi, I. Shames, and N. Batterham
Journal Papers Control Engineering Practice, 67, pp. 13–20, 2017.

#### Abstract

Networked control systems with encrypted sensors measurements is considered. Semi-homomorphic encryption, specifically the Paillier encryption, is used so that the controller can perform the required computation on the encrypted data. Conditions on the parameters of the encryption technique are provided that guarantee the stability and the performance of the closed-loop system. The results are subsequently extended Laplacian based distributed systems, such as formation-seeking algorithms. It is shown that the problem of figuring out the state measurements of the neighbouring agents of a compromised agent upon using the proposed algorithm is numerically intractable.

#### [J14] Preserving Privacy of Finite Impulse Response Systems

G. Bottegal, F. Farokhi, and I. Shames
Journal Papers IEEE Control Systems Letters, 1(1), pp. 128-133, 2017.

#### Abstract

The problem of adding input and output noises for increasing the model identification error of finite impulse response (FIR) systems is considered. This is motivated by the desire of the designer to protect the model of the closed-loop system as a trade secret by rendering model identification techniques ineffective.} An optimal filter for constructing additive noises that maximizes the identification error subject to the closed-loop performance degradation being kept below a given limit is proposed. This is done for both known and unknown inputs. For the latter, the statistics of the input are required. Alternatively, differential privacy is used for designing output noises that preserve the privacy of the model. Although differential privacy provides strong guarantees on preserving the privacy, it is less suitable in comparison to the other method as it lacks a systematic way to select its parameters and restricts the additive noise to Laplace, which makes the integration of the closed-loop systems with other control loops difficult.

#### [J13] Security Analysis of Cyber-Physical Systems Using ${\small\mathcal{H}_2}$ Norm

I. Shames, F. Farokhi, and T. H. Summers
Journal Papers IET Control Theory & Applications, 11 (11), pp. 1749-1755, 2017.

#### Abstract

In this paper, we study the effect of attacks on networked systems and propose a new security index to analyze the impact of such attacks using ${\small\mathcal{H}_2}$ norms of attacks to target and monitoring outputs. In addition, we pose, and subsequently solve, optimization problems for selecting inputs or outputs that point to attacks with maximum impact and least detectability. To demonstrate the applicability of the analysis methods proposed in this paper IEEE 9-bus and 50-generator 145-bus systems are considered as test cases.

#### [J12] Estimation with Strategic Sensors

F. Farokhi, A. M. H. Teixeira, and C. Langbort
Journal Papers IEEE Transactions on Automatic Control, 62(2), pp. 724-739, 2017.

#### Abstract

We introduce a model of estimation in the presence of strategic, self-interested sensors. We employ a game-theoretic setup to model the interaction between the sensors and the receiver. The cost function of the receiver is equal to the estimation error variance while the cost function of the sensor contains an extra term which is determined by its private information. We start by the single sensor case in which the receiver has access to a noisy but honest side information in addition to the message transmitted by a strategic sensor. We study both static and dynamic estimation problems. For both these problems, we characterize a family of equilibria in which the sensor and the receiver employ simple strategies. Interestingly, for the dynamic estimation problem, we find an equilibrium for which the strategic sensor uses a memory-less policy. We generalize the static estimation setup to multiple sensors with synchronous communication structure (i.e., all the sensors transmit their messages simultaneously). We prove the maybe surprising fact that, for the constructed equilibrium in affine strategies, the estimation quality degrades as the number of sensors increases. However, if the sensors are herding (i.e., copying each other policies), the quality of the receiver's estimation improves as the number of sensors increases. Finally, we consider the asynchronous communication structure (i.e., the sensors transmit their messages sequentially).

#### [J11] Faithful Implementations of Distributed Algorithms and Control Laws

T. Tanaka, F. Farokhi, and C. Langbort
Journal Papers IEEE Transactions on Control of Network Systems, 4(2), pp. 191-201, 2017.

#### Abstract

When a distributed algorithm must be executed by strategic agents with misaligned interests, a social leader needs to introduce an appropriate tax/subsidy mechanism to incentivize agents to faithfully implement the intended algorithm so that a correct outcome is obtained. We discuss the incentive issues of implementing economically efficient distributed algorithms using the framework of indirect mechanism design theory. In particular, we show that indirect Groves mechanisms are not only sufficient but also necessary to achieve incentive compatibility. This result can be viewed as a generalization of the Green-Laffont theorem to indirect mechanisms. Then we introduce the notion of asymptotic incentive compatibility as an appropriate solution concept to faithfully implement distributed and iterative optimization algorithms. We consider two special types of optimization algorithms: dual decomposition algorithms for resource allocation and average consensus algorithms.

#### [J10] On Reconstructability of Quadratic Utility Functions from the Iterations in Gradient Methods

F. Farokhi, I. Shames, M. G. Rabbat, and M. Johansson
Journal Papers Automatica, 66, pp. 254–261, 2016.

#### Abstract

In this paper, we consider a scenario where an eavesdropper can read the content of messages transmitted over a network. The nodes in the network are running a gradient algorithm to optimize a quadratic utility function where such a utility optimization is a part of a decision making process by an administrator. We are interested in understanding the conditions under which the eavesdropper can reconstruct the utility function or a scaled version of it and, as a result, gain insight into the decision-making process. We establish that if the parameter of the gradient algorithm, i.e.,~the step size, is chosen appropriately, the task of reconstruction becomes practically impossible for a class of Bayesian filters with uniform priors. We establish what step-size rules should be employed to ensure this.

#### [J9] A Piecewise-Constant Congestion Taxing Policy for Repeated Routing Games

F. Farokhi and K. H. Johansson
Journal Papers Transportation Research: Part B, 78, pp. 123–143, 2015.

#### Abstract

In this paper, we consider repeated routing games with piecewise-constant congestion taxing in which a central planner sets and announces the congestion taxes for fixed windows of time in advance. Specifically, congestion taxes are calculated using marginal congestion pricing based on the flow of the vehicles on each road prior to the beginning of the taxing window (and, hence, there is a time-varying delay in setting the congestion taxes). We motivate the piecewise-constant taxing policy by that users or drivers may dislike fast-changing prices and that they also prefer prior knowledge of the prices. We prove for this model that the multiplicative update rule and the discretized replicator dynamics converge to a socially optimal flow when using vanishing step sizes. Considering that the algorithm cannot adapt itself to a changing environment when using vanishing step sizes, we propose adopting constant step sizes in this case. Then, however, we can only prove the convergence of the dynamics to a neighborhood of the socially optimal flow (with the size of the neighbourhood being of the order of the selected step size). The results are illustrated on a nonlinear version of Pigou’s famous routing game.

#### [J8] Promoting Truthful Behaviour in Participatory-Sensing Mechanisms

F. Farokhi, I. Shames, and M. Cantoni
Journal Papers IEEE Signal Processing Letters, 22(10), pp. 1538–1542, 2015.

#### Abstract

In this paper, the interplay between a class of nonlinear estimators and strategic sensors is studied in several participatory-sensing scenarios. It is shown that for the class of estimators, if the strategic sensors have access to noiseless measurements of the to-be-estimated-variable, truth-telling is an equilibrium of the game that models the interplay between the sensors and the estimator. Furthermore, performance of the proposed estimators is examined in the case that the strategic sensors form coalitions and in the presence of noise.

#### [J7] A Study of Truck Platooning Incentives Using a Congestion Game

F. Farokhi and K. H. Johansson
Journal Papers IEEE Transactions on Intelligent Transportation Systems, 16(2), pp. 581–595, 2015.

#### Abstract

We introduce an atomic congestion game with two types of agents, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a trade-off between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they pay for using the road. In addition to these terms, the trucks have an incentive for using the road at the same time as their peers because they have platooning capabilities, which allow them to save fuel. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm to validate parts of the modeling assumptions and extract reasonable parameters for the simulations. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategy Nash equilibrium of this game. We perform a comprehensive simulation study to understand the influence of various factors, such as the drivers' value of time and the percentage of the trucks that are equipped with platooning devices, on the properties of the Nash equilibrium.

#### [J6] Optimal Control Design under Limited Model Information for Discrete-Time Linear Systems with Stochastically-Varying Parameters

F. Farokhi and K. H. Johansson
Journal Papers IEEE Transactions on Automatic Control, 60(3), pp. 684–699, 2015.

#### Abstract

The value of plant model information available in the control design process is discussed. We design optimal state-feedback controllers for interconnected discrete-time linear systems with stochastically-varying parameters. The parameters are assumed to be independently and identically distributed random variables in time. The design of each controller relies only on (i) exact local plant model information and (ii) statistical beliefs about the model of the rest of the system. We consider both finite-horizon and infinite-horizon quadratic cost functions. The optimal state-feedback controller is derived in both cases. The optimal controller is shown to be linear in the state and to depend on the model parameters and their statistics in a particular way. Furthermore, we study the value of model information in optimal control design using the performance degradation ratio which is defined as the supremum (over all possible initial conditions) of the ratio of the cost of the optimal controller with limited model information scaled by the cost of the optimal controller with full model information. An upper bound for the performance degradation ratio is presented for the case of fully-actuated subsystems. Comparisons are made between designs based on limited, statistical, and full model information. Throughout the paper, we use a power network example to illustrate concepts and results.

#### [J5] Adaptive Control Design under Structured Model Information Limitation: A Cost-Biased Maximum-Likelihood Approach

F. Farokhi and K. H. Johansson
Journal Papers Systems & Control Letters, 75, pp. 8–13, 2015.

#### Abstract

Networked control strategies based on limited information about the plant model usually results in worse closed-loop performance than optimal centralized control with full plant model information. Recently, this fact has been established by utilizing the concept of competitive ratio, which is defined as the worst case ratio of the cost of a control design with limited model information to the cost of the optimal control design with full model information. We show that an adaptive controller, inspired by a controller proposed by Campi and Kumar, with limited plant model information, asymptotically achieves the closed-loop performance of the optimal centralized controller with full model information for almost any plant. Therefore, there exists, at least, one adaptive control design strategy with limited plant model information that can achieve a competitive ratio equal to one. The plant model considered in the paper belongs to a compact set of stochastic linear time-invariant systems and the closed loop performance measure is the ergodic mean of a quadratic function of the state and control input. We illustrate the applicability of the results numerically on a vehicle platooning problem.

#### [J4] Stochastic Sensor Scheduling for Networked Control Systems

F. Farokhi and K. H. Johansson
Journal Papers IEEE Transactions on Automatic Control, 59(5), pp. 1147–1162, 2014.

#### Abstract

Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost function for this Markov chain as the summation of terms depending on the average sampling frequencies of the subsystems and the effort needed for changing the parameters of the underlying Markov chain. By minimizing this cost function through extending Brockett's recent approach to optimal control of Markov chains, we extract an optimal scheduling policy to fairly allocate the network resources among the control loops. We study the statistical properties of this scheduling policy in order to compute upper bounds for the closed-loop performance of the networked system, where several decoupled scalar subsystems are connected to their corresponding estimator or controller through a shared communication medium. We generalize the estimation results to observable subsystems of arbitrary order. Finally, we illustrate the developed results numerically on a networked system composed of several decoupled water tanks.

#### [J3] Decentralized Disturbance Accommodation with Limited Plant Model Information

F. Farokhi, C. Langbort, and K. H. Johansson
Journal Papers SIAM Journal on Control and Optimization, 51(2), pp. 1543–1573, 2013.

#### Abstract

The design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is considered in this paper. Their closed-loop performance are compared using a performance metric called competitive ratio which is the worst-case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information. It was recently shown that when it comes to designing optimal centralized or partially structured decentralized state-feedback controllers with limited model information, the best control design strategy in terms of competitive ratio is a static one. This is true even though the optimal structured decentralized state-feedback controller with full model information is dynamic. In this paper, we show that, in contrast, the best limited model information control design strategy for the disturbance accommodation problem gives a dynamic controller. We find an explicit minimizer of the competitive ratio and we show that it is undominated, that is, there is no other control design strategy that performs better for all possible plants while having the same worst-case ratio. This optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For constant disturbances, it is shown that this structure corresponds to proportional-integral control.

#### [J2] Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems

F. Farokhi, C. Langbort, and K. H. Johansson
Journal Papers Automatica, 49(2), pp. 326–337, 2013.

#### Abstract

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant’s model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Finally, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

#### [J1] Optimal State-Feedback Design for Nonlinear Feedback-Linearizable Systems

P. Mohajerin-Esfahani, F. Farokhi, and M. Karimi-Ghartemani
Journal Papers IET Control Theory & Applications, 5(2), pp. 323–333, 2011.

#### Abstract

This paper addresses the problem of optimal state-feedback design for a class of non-linear systems. The method is applicable to all non-linear systems which can be linearised using the method of state-feedback linearisation. The alternative is to use linear optimisation techniques for the linearised equations, but then there is no guarantee that the original non-linear system behaves optimally. The authors use feedback linearisation technique to linearise the system and then design a state feedback for the feedback-linearised system in such a way that it ensures optimal performance of the original non-linear system. The method cannot ensure global optimality of the solution but the global stability of the non-linear system is ensured. The proposed method can optimise any arbitrary smooth function of states and input, including the conventional quadratic form. The proposed method can also optimise the feedback linearising transformation. The method is successfully applied to control the design of a flexible joint dynamic and the results are discussed. Compared with the conventional linear quadratic regulator (LQR) technique, the minimum value of cost function is significantly reduced by the proposed method.

#### [C45] Nonstochastic Channel Models for Bounded State Estimation and Control

A. Saberi, F. Farokhi, G. Nair
Conference Papers Invited Presentation at 2018 56th Annual Allerton Conference on Communication, Control, and Computing, 2018.

#### [C44] Bilateral Trade under Information Asymmetry and Quantized Measurements

F. Farokhi and I. Shames
Conference Papers in Proceedings of the 57th IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, December 17-19, 2018.

#### Abstract

Bilateral trading games are considered in which the buyer has access to more accurate information about the seller's valuation. The accuracy of the information, acquired by the buyer, is captured using quantization levels. We study how the level of accuracy and the rule for setting the final price in the bilateral trade game change the probability of striking a deal between the parties as well as the expected payoff of various parties. We also quantify the information level that maximizes the gain in the payoff for the smallest price of research assuming that acquiring accurate information is costly.

#### [C43] Secure Control of Nonlinear Systems Using Semi-Homomorphic Encryption

Y. Lin, F. Farokhi, I. Shames, D. Nesic
Conference Papers in Proceedings of the 57th IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, December 17-19, 2018.

#### Abstract

A secure nonlinear networked control systems (NCSs) design using semi-homomorphic encryption, namely, Pailier encryption is studied. Under certain assumptions, control signal computation using encrypted signal directly is allowed by semi-homomorphic encryption. Thus, the security of the NCSs is further enhanced by concealing information on the controller side. However, additional technical difficulties in the design and analysis of NCSs are induced compared to standard NCSs. In this paper, the stabilization of a nonlinear discrete time NCS is considered. More specifically, sufficient conditions on the encryption parameters that guarantee stability of the NCS are provided, and a trade-off between the encryption parameters and the closed loop performance are shown.

#### [C42] On Privacy of Quantized Sensor Measurements through Additive Noise

C. Murguia, I. Shames, D. Nesic, and F. Farokhi
Conference Papers in Proceedings of the 57th IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, December 17-19, 2018.

#### Abstract

We study the problem of maximizing privacy of quantized sensor measurements by adding random variables. In particular, we consider the setting where information about the state of a process is obtained using noisy sensor measurements. This information is quantized and sent to a remote station through an unsecured communication network. It is desired to keep the state of the process private; however, because the network is not secure, adversaries might have access to sensor information, which could be used to estimate the process state. To avoid an accurate state estimation, we add random numbers to the quantized sensor measurements and send the sum to the remote station instead. The distribution of these random variables is designed to minimize the mutual information between the sum and the quantized sensor measurements for a desired level of distortion -- how different the sum and the quantized sensor measurements are allowed to be. Simulations are presented to illustrate our results.

#### [C41] Security versus Privacy

F. Farokhi and P. M. Esfahani
Conference Papers in Proceedings of the 57th IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, December 17-19, 2018.

#### Abstract

Linear queries can be submitted to a server containing private data. The server provides a response to the queries systematically corrupted using an additive noise to preserve the privacy of those whose data is stored on the server. The measure of privacy is inversely proportional to the trace of the Fisher information matrix. It is assumed that an adversary can inject a false bias to the responses. The measure of the security, capturing the ease of detecting the presence of the false data injection, is the sensitivity of the Kullback-Leiber divergence to the additive bias. An optimization problem for balancing privacy and security is proposed and subsequently solved. It is shown that the level of guaranteed privacy times the level of security equals a constant. Therefore, by increasing the level of privacy, the security guarantees can only be weakened and vice versa. Similar results are developed under the differential privacy framework.

#### [C40] Estimation and Control over a Nonstochastic Binary Erasure Channel

A. Saberi, F. Farokhi, G. Nair
Conference Papers in Proceedings of the 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys18), Groningen, the Netherlands, August 27-28, 2018.

#### Abstract

This paper considers a binary channel which erases up to a given number of bit in each consecutive block of given length, without any statistical structure. Nonzero upper and lower bounds on the zero-error capacity of the channel are found, as well as an exact expression for its zero-error capacity with perfect feedback. The results are compared with the stochastic case, and then used to find separate necessary and sufficient conditions to be able to uniformly estimate and control the states of a linear system with bounded noise via the channel.

#### [C39] Scalable Iterations for Solving Constrained LQ Control Problems with Cascade Dynamics

M. Cantoni, A. Zafar, and F. Farokhi
Conference Papers in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Hong Kong, July 16-20, 2018.

#### Abstract

This paper is about the computation of constrained optimal controls for series interconnections of heterogeneous sub-systems with linear discrete-time dynamics. The optimal control problem is first formulated in a form that is amenable to iterative solution by the alternating direction method of multipliers. It is observed that this technique yields per-iteration computational burden that scales linearly in the both the number of systems along the cascade and the length of the time-horizon. Moreover, parallelization of the computation across a network of processors is possible with an information exchange architecture that mirrors the cascade structure of the system. Recent work that also exploits temporal and spatial structure within interior point methods for the problem, achieves per-iteration computational cost that scales linearly in the cascade length, but cubically in the length of the time horizon. On the other hand, interior point methods will typically take significantly fewer iterations to converge than the proposed first order method. With this in mind, convergence of the latter is explored numerically as the number of sub-systems and time horizon are varied.

#### [C38] Security Analysis of Quantized Bayesian Estimators

F. Farokhi, D. Selvaratnam, and I. Shames
Conference Papers in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Hong Kong, July 16-20, 2018.

#### Abstract

Security of networked Bayesian source localization algorithms is analysed in this paper. The Bayesian estimators construct the probability density function of the location of the source from quantised measurements. Understanding fundamental limits in the performance of an adversary for manipulating the posterior of the Bayesian estimator is the main focus of the paper. The analysis is performed for the cases where the estimator is not aware of the presence of the adversary. The results are then generalized to the case where the estimator is aware of the attacker.

#### [C37] Secure State Estimation Using Semihomomporphic Encryption

M. Zamani, L. Sadeghikhorrami, A. A. Safavi, and F. Farokhi
Conference Papers in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Hong Kong, July 16-20, 2018.

#### Abstract

This paper is concerned with estimation in a networked control system environment. In particular, secure state estimation using a Leunberger estimator over a network is considered. The Paillier encryption, which is a semi-homomorphic encryption method, is employed so that the algebraic calculations required for the estimation can be performed over the encrypted data. This enhances the security of the state estimation process. Conditions are presented under which the stability of the resultant encrypted estimator is ensured. A numerical example is utilized to demonstrate the theoretical results.

#### [C36] Compressive Sensing in Fault Detection

F. Farokhi and I. Shames
Conference Papers in Proceedings of the American Control Conference, Milwaukee, WI, USA, June 27-29, 2018.

#### Abstract

Randomly generated tests are used to identify faulty sensors in large-scale discrete-time linear time-invariant dynamical systems with high probability. It is proved that the number of the required tests for successfully identifying the location of the faulty sensors (with high probability) scales logarithmically with the number of the sensors and quadratically with the maximum number of faulty sensors. It is also proved that the problem of decoding the identity of the faulty sensors based on the random tests can be cast as a linear programming problem and therefore can be solved reliably and efficiently even for large-scale systems. A numerical example based on automated irrigation networks is utilized to demonstrate the results.

#### [C35] Optimal Constrained Additive Noise Distribution Minimizing Fisher Information for Ensuring Privacy

F. Farokhi and H. Sandberg
Conference Papers in Proceedings of the 56th IEEE Conference on Decision and Control (CDC), Melbourne, Australia, 12-15 December 2017.

#### Abstract

The problem of preserving the privacy of individual entries of a database with constrained additive noise is considered. An adversary can submit linear queries to an agent possessing the entire database. The agent returns a response to the query that is corrupted by an additive random noise whose support is a subset or equal to a constraint set. The Cramér-Rao bound is used to bound the variance of the estimation error of any unbiased estimators of the database, which may be used by the adversary, to the trace of the inverse of the Fisher information matrix. A measure of privacy using the Fisher information matrix is developed. The probability density that minimizes the Fisher information (as a proxy for maximizing the measure of privacy) is computed.

#### [C34] Preserving Privacy of Finite Impulse Response Systems

G. Bottegal, F. Farokhi, and I. Shames
Conference Papers in Proceedings of the 56th IEEE Conference on Decision and Control (CDC), Melbourne, Australia, 12-15 December 2017.

#### Abstract

The problem of adding input and output noises for increasing the model identification error of finite impulse response (FIR) systems is considered. This is motivated by the desire of the designer to protect the model of the closed-loop system as a trade secret by rendering model identification techniques ineffective.} An optimal filter for constructing additive noises that maximizes the identification error subject to the closed-loop performance degradation being kept below a given limit is proposed. This is done for both known and unknown inputs. For the latter, the statistics of the input are required. Alternatively, differential privacy is used for designing output noises that preserve the privacy of the model. Although differential privacy provides strong guarantees on preserving the privacy, it is less suitable in comparison to the other method as it lacks a systematic way to select its parameters and restricts the additive noise to Laplace, which makes the integration of the closed-loop systems with other control loops difficult.

#### [C33] Private and Secure Coordination of Match-Making for Heavy-Duty Vehicle Platooning

F. Farokhi, Iman Shames, Karl H. Johansson
Conference Papers in Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), Toulouse, France, 9-14 July 2017.

#### Abstract

A secure and private framework for inter-agent communication and coordination is developed. This allows an agent, in our case a fleet owner, to ask questions or submit queries in an encrypted fashion using semi-homomorphic encryption. The submitted query can be about the interest of the other fleet owners for using a road at a specific time of the day, for instance, for the purpose of collaborative vehicle platooning. The other agents can then provide appropriate responses without knowing the content of the questions or the queries. Strong privacy and security guarantees are provided for the agent who is submitting the queries. It is also shown that the amount of the information that this agent can extract from the other agent is bounded. In fact, with submitting one query, a sophisticated agent can at most extract the answer to two queries. This secure communication platform is used subsequently to develop a distributed coordination mechanisms among fleet owners.

#### [C32] A Scalable QP Solver for Optimal Control of Cascades with Constraints

M. Cantoni, F. Farokhi, E. Kerrigan, I. Shames
Conference Papers in Proceedings of the Australian Control Conference (AUCC 2016), Newcastle, Australia, November 3-4, 2016.

#### Abstract

A finite-horizon linear-quadratic control problem is studied. The structure of this problem is such that the input constraints, state constraints and performance index all separate across the underlying cascade of dynamical sub-systems. An equivalent quadratic program is formulated, for which an interior-point method is devised. The computational burden of this method scales linearly with the number of sub-systems. By contrast, the computational burden scales cubically with the time horizon. Therefore, the approach is of use when the number of sub-systems is large relative to the time horizon.

#### [C31] Privacy-Constrained Communication

F. Farokhi and G. Nair
Conference Papers in Proceedings of the 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys 2016), Tokyo, Japan, September 8-9, 2016.

#### Abstract

A game is introduced to study the effect of privacy in strategic communication between a well-informed sender and a receiver. The receiver wants to accurately estimate a random variable. The sender, however, wants to communicate a message that balances a trade-off between providing an accurate measurement and minimizing the amount of leaked private information, which is assumed to be correlated with the to-be-estimated variable. The mutual information between the transmitted message and the private information is used as a measure of the amount of leaked information. An equilibrium is constructed and its properties are investigated.

#### [C30] Secure and Private Cloud-Based Control Using Semi-Homomorphic Encryption

F. Farokhi, I. Shames, and N. Batterham
Conference Papers in Proceedings of the 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys 2016), Tokyo, Japan, September 8-9, 2016.

#### Abstract

Networked control systems with encrypted sensors measurements is considered. Semi-homomorphic encryption is used so that the controller can perform the required computation on the encrypted data. Specifically, in this paper, the Paillier encryption technique is utilized that allows summation of decrypted data to be performed by multiplication of the encrypted data. Conditions on the parameters of the encryption technique are provided that guarantee the stability of the closed-loop system and ensure certain bounds on the closed-loop performance.

#### [C29] Optimal State Estimation with Measurements Corrupted by Laplace Noise

F. Farokhi, J. Milosevic, and H. Sandberg
Conference Papers in Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016), Las Vegas, NV, USA, December 12-14, 2016.

#### Abstract

Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by a Laplace noise. The optimal least mean square estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as a Gaussian noise scaled by a Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator and the maximum a posteriori (MAP) estimate of the state.

#### [C28] Preserving Privacy of Agents in Participatory-Sensing Schemes for Traffic Estimation

F. Farokhi and I. Shames
Conference Papers in Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016), Las Vegas, NV, USA, December 12-14, 2016.

#### Abstract

A measure of privacy infringement for agents (or participants) travelling across a transportation network in participatory-sensing schemes for traffic estimation is introduced. The measure is defined to be the conditional probability that an external observer assigns to the private nodes in the transportation network, e.g., location of home or office, given all the position measurements that it broadcasts over time. An algorithm for finding an optimal trade-off between the measure of privacy infringement and the expected estimation error, captured by the number of the nodes over which the participant stops broadcasting its position, is proposed. The algorithm searches over a family of policies in which an agent stops transmitting its position measurements if its distance (in terms of the number of hops) to the privacy sensitive node is smaller than a prescribed threshold. Employing such symmetric policies are advantageous in terms of the resources required for implementation and the ease of computation. The results are expanded to more general policies. Further, the effect of the heterogeneity of the population density on the optimal policy is explored. Finally, the relationship between the betweenness measure of centrality and the optimal privacy-preserving policy of the agents is numerically explored.

#### [C27] Guaranteed Maximum Power Point Tracking by Scalar Iterations with Quadratic Convergence Rate

I. Shames, F. Farokhi, and M. Cantoni
Conference Papers in Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016), Las Vegas, NV, USA, December 12-14, 2016.

#### Abstract

In this paper the problem of maximum power point tracking (MPPT) is considered. We show that the problem has a unique solution and it can be reduced to the problem of finding the unique root of a single variable scalar function. We show that Newton's iterations can be applied to the problem of finding this root quadratically fast for an initialisation that is independent of the parameters of the MPPT problem. The results of applying the approach to 1,000,000 randomly-generated instances of the MPPT problem are presented and consistency with the analysis is observed.

#### [C26] A Game-Theoretic Approach to Scheduling Rigid Demands on Dynamical Systems

F. Farokhi, M. Cantoni, and I. Shames
Conference Papers in Proceedings of the Australian Control Conference (AUCC 2016), Newcastle, Australia, November 3-4, 2016.

#### Abstract

A game-theoretic approach to solving a load scheduling problem is explored. Specifically, we consider the problem of scheduling rigid load requests on a constrained discrete-time linear time-invariant dynamical system. Load requests are rigid in the sense that it is only possible to delay them when forming a feasible schedule; the profile of each request is fixed. A game is devised to encode the trade-off between users' sensitivities to scheduling delays and the need to respect the constraints on the dynamic response of the system to the schedule over a given planning horizon. It is shown that for a particular pricing mechanism the optimal schedule is an equilibrium of the game. Established game-theoretic learning algorithms can therefore be used to devise distributed methods for recovering the optimal schedule. A numerical example involving the operation of an automated irrigation channel is presented.

#### [C25] Distributed Negotiation for Scheduling Smart Appliances

F. Farokhi and M. Cantoni
Conference Papers in Proceedings of the Australian Control Conference (AUCC 2015), Gold Coast, Australia, November 5-6, 2015.

#### Abstract

A framework is presented for scheduling smart appliances based on electricity prices and constraints, such as timing of service, delays between phases of operation and working regimes, and maximum permissible power consumption. We use game theory to construct a distributed algorithm for negotiating the optimal schedule for the appliances.

#### [C24] Conditions and Strategies for Uniqueness of the Solutions to Cooperative Localization and Mapping Problems Using Rigidity Theory

I. Shames, T. H. Summers, F. Farokhi, R. C. Shekhar
Conference Papers in Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, December 15-18, 2015.

#### Abstract

In this paper, we use the rigidity theory to address two problems encountered in cooperative localization and mapping. First, we consider the problem of map merging in scenarios where a group of mobile agents explore an environment. We establish conditions for the agents to be able to exchange the environmental information that they have gathered in their own local coordinate frames. We relate these conditions to the sensing capabilities of the agents. Second, we study a scenario where a group of mobile agents in a network need to localize their positions. It is assumed that there are not enough measurements to achieve this task at any time instance. We propose a coordinated motion strategy that enables the agents to achieve this goal over a period of time. Numerical simulations are provided to demonstrate the results.

#### [C23] Scheduling Rigid Demands on Continuous-Time Linear Shift-Invariant Systems

F. Farokhi, M. Cantoni, and I. Shames
Conference Papers in Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, December 15-18, 2015.

#### Abstract

We consider load scheduling on constrained continuous-time linear dynamical systems, such as automated irrigation and other distribution networks. The requested loads are rigid, i.e., the shapes cannot be changed. Hence, it is only possible to shift the order back-and-forth in time to arrive at a feasible schedule. We present a numerical algorithm based on using log-barrier functions to include the state constraints in the social cost function (i.e., an appropriate function of the scheduling delays). This algorithm requires a feasible initialization. Further, in another algorithm, we treat the state constraints as soft constraints and heavily penalize the constraint violations. This algorithm can even be initialized at an infeasible point. The applicability of both these numerical algorithms is demonstrated on an automated irrigation network with two pools and six farms.

#### [C22] Quadratic Gaussian Privacy Game

F. Farokhi, H. Sandberg, I. Shames, and M. Cantoni
Conference Papers in Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, December 15-18, 2015.

#### Abstract

A game-theoretic model for analysing the effects of privacy on strategic communication between agents is devised. In the model, a sender wishes to provide an accurate measurement of the state to a receiver while also protecting its private information (which is correlated with the state) private from a malicious agent that may eavesdrop on its communications with the receiver. A family of nontrivial equilibria, in which the communicated messages carry information, is constructed and its properties are studied.

#### [C21] Cooperation Patterns between Fleet Owners for Transport Assignments

F. Farokhi, K.-Y. Liang, and K. H. Johansson
Conference Papers in Proceedings of the IEEE Multi-Conference on Systems and Control (MSC 2015), Sydney, Australia, September 21-23, 2015.

#### Abstract

We study cooperation patterns between the heavy-duty vehicle fleet owners to reduce their costs, improve their fuel efficiency, and decrease their emissions. We consider a distributed cooperation pattern in which the fleet owners can communicate directly with each other to form alliances. A centralized cooperation pattern is studied in which the fleet owners pay to subscribe to a third-party service provider that pairs their vehicles for cooperation. The effects of various pricing strategies on the behaviour of fleet owners and their inclusiveness are analyzed. It is shown that the fleet size has an essential role.

#### [C20] Using Piecewise-Constant Congestion Taxing Policy in Repeated Routing Games

F. Farokhi and K. H. Johansson
Conference Papers in Proceedings of SIAM Conference on Control and Its Applications (SIAM CT 15), Paris, France, July 8-10, 2015.

#### Abstract

We consider repeated routing games with piecewise-constant congestion taxing in which a central planner sets and announces the congestion taxes for fixed windows of time in advance. Specifically, congestion taxes are calculated using marginal congestion pricing based on the flow of the vehicles on each road prior to the beginning of the taxing window. The piecewise-constant taxing policy in motivated by that users or drivers may dislike fast-changing prices and that they also prefer prior knowledge of the prices. We prove that the multiplicative update rule converges to a socially optimal flow when using vanishing step sizes. Considering that the algorithm cannot adapt itself to a changing environment when using vanishing step sizes, we propose using constant step sizes in this case. Then, however, we can only prove the convergence of the dynamics to a neighborhood of the socially optimal flow (with its size being of the order of the selected step size).

#### [C19] SiMpLIfy: A Toolbox for Structured Model Reduction

M. Biel, F. Farokhi, and H. Sandberg
Conference Papers in Proceedings of European Control Conference (ECC 2015), Linz, Austria, July 15-17, 2015.

#### Abstract

In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured model reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various model reduction methods in the toolbox on a structured mass-spring mechanical system.

#### [C18] Investigating the Interaction Between Traffic Flow and Vehicle Platooning Using a Congestion Game

F. Farokhi and K. H. Johansson
Conference Papers in Proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC), Cape Town, South Africa, August 24-29, 2014.

#### Abstract

We consider a congestion game with two types of agents to describe the traffic flow on a road at various time intervals in each day. The first type of agents (cars) maximize a utility which is determined by a sum of a penalty for using the road at a time other than their preferred time interval, the average velocity of the traffic flow, and the congestion tax. The second type of agents (trucks or heavy-duty vehicles) can benefit from using the road together with other second-type agents. This is because the trucks can form platoons to save fuel through reducing the air drag force. We study a Nash equilibrium of this game to study the interaction between the traffic flow and the platooning incentives. We prove that the introduced congestion game does not admit a potential function unless we devise an appropriate congestion taxing policy. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategic Nash equilibrium of this congestion game. Lastly, we demonstrate the developed results on a numerical example using data from a highway segment in Stockholm.

#### [C17] Gaussian Cheap Talk Game with Quadratic Cost Functions: When Herding between Strategic Senders is a Virtue

F. Farokhi, A. M. H. Teixeira, C. Langbort
Conference Papers in Proceedings of American Control Conference (ACC 2014), Portland, Oregon, USA, June 4-6, 2014.

#### Abstract

We consider a Gaussian cheap talk game with quadratic cost functions. The cost function of the receiver is equal to the estimation error variance, however, the cost function of each senders contains an extra term which is captured by its private information. Following the cheap talk literature, we model this problem as a game with asymmetric information. We start by the single sender case in which the receiver also has access to a noisy but honest side information in addition to the message transmitted by a strategic sender. We generalize this setup to multiple sender case. For the multiple sender case, we observe that if the senders are not herding (i.e., copying each other policies), the quality of the receiver's estimation degrades rapidly as the number of senders increases.

#### [C16] Crowd-Sourcing Estimation with Strategic Senders

F. Farokhi, A. M. H. Teixeira, and C. Langbort
Conference Papersin Proceedings of Swedish Control Conference (Reglermöte 2014), Linköping, Sweden, June 2-3, 2014.

#### Abstract

We model the problem of crowd-sourcing estimation with strategic senders using a Gaussian cheap talk game with quadratic cost functions. The cost function of the receiver is equal to the estimation error variance, however, the cost function of each senders contains an extra term which is captured by its private information. Interestingly, we observe that if the senders are not herding (i.e., copying each other policies), the quality of the receiver's estimation degrades rapidly as the number of senders increases. However, if the senders herd, the estimation quality improves by admitting more senders.

#### [C15] A Heterogeneous Routing Game

F. Farokhi, W. Krichene, A. M. Bayen, and K. H. Johansson
Conference Papers in Proceedings of Annual Allerton Conference on Communication, Control, and Computing (Allerton 2013), Monticello, Illinois, USA, October 2-4, 2013.

#### Abstract

Most literature on routing games make the as- sumption that drivers or vehicles are of the same type and, hence, experience the same latency or cost when traveling along the edges of the network. In contrast, in this article, we propose a heterogeneous routing game in which each driver or vehicle belongs to a certain type. The type determines the cost of traveling along an edge as a function of the flow of all types of drivers or vehicles over that edge. We examine the existence of a Nash equilibrium in this heterogeneous routing game. We study the conditions for which the problem of finding a Nash equilibrium can be posed as a convex optimization problem and is therefore numerically tractable. Numerical simulations are presented to validate the results.

#### [C14] A Faithful Distributed Implementation of Dual Decomposition and Average Consensus Algorithms

T. Tanaka, F. Farokhi and C. Langbort
Conference Papers in Proceedings of the 52nd IEEE Conference on Decision and Control (CDC 2013), Florence, Italy, December 10-13, 2013.

#### Abstract

We consider large scale cost allocation problems and consensus seeking problems for multiple agents, in which agents are suggested to collaborate in a distributed algorithm to find a solution. If agents are strategic to minimize their own individual cost rather than the global social cost, they are endowed with an incentive not to follow the intended algorithm, unless the tax/subsidy mechanism is carefully designed. Inspired by the classical Vickrey-Clarke-Groves mechanism and more recent algorithmic mechanism design theory, we propose a tax mechanism that incentivises agents to faithfully implement the intended algorithm. In particular, a new notion of asymptotic incentive compatibility is introduced to characterize a desirable property of such class of mechanisms. The proposed class of tax mechanisms provides a sequence of mechanisms that gives agents a diminishing incentive to deviate from suggested algorithm.

#### [C13] Optimal H∞ Control Design under Model Information Limitations and State Measurement Constraints

F. Farokhi, H. Sandberg, and K. H. Johansson
Conference Papers in Proceedings of the 52nd IEEE Conference on Decision and Control (CDC 2013), Florence, Italy, December 10-13, 2013.

#### Abstract

We present a suboptimal control design algorithm for a family of continuous-time parameter-dependent linear systems that are composed of interconnected subsystems. We are interested in designing the controller for each subsystem such that it only utilizes partial state measurements (characterized by a directed graph called the control graph) and limited model parameter information (characterized by the design graph). The algorithm is based on successive local minimizations and maximizations (using the subgradients) of the H-infinity norm of the closed-loop transfer function with respect to the controller gains and the system parameters. We use a vehicle platooning example to illustrate the applicability of the results.

#### [C12] A Game-Theoretic Framework for Studying Truck Platooning Incentives

F. Farokhi and K. H. Johansson
Conference Papers in Proceedings of the 16th International IEEE Annual Conference on Intelligent Transportation Systems (ITSC 2013), The Hague, The Netherlands, October 6 - 9, 2013.

#### Abstract

An atomic congestion game with two types of agents, cars and trucks, is used to model the traffic flow on a road over certain time intervals. In this game, the drivers make a trade-off between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they are paying to use the road. The trucks have platooning capabilities and therefore, have an incentive for using the road at the same time as their peers. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm to validate the modeling assumptions and extract reasonable parameters for the simulations. We perform a comprehensive simulation study to understand the influence of various factors, such as the percentage of the trucks that are equipped with platooning devices on the properties of the pure strategy Nash equilibrium that is learned using a joint strategy fictitious play.

#### [C11] Networked Estimation Using Sparsifying Basis Prediction

F. Farokhi, A. Shirazinia and K. H. Johansson
Conference Papers in Proceedings of the 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys 2013), Koblenz, Germany, September 25 - 26, 2013.

#### Abstract

We present a framework for networked state estimation, where systems encode their (possibly high dimensional) state vectors using a mutually agreed basis between the system and the estimator (in a remote monitoring unit). The basis sparsifies the state vectors, i.e., it represents them using vectors with few non-zero components, and as a result, the systems might need to transmit only a fraction of the original information to be able to recover the non-zero components of the transformed state vector. Hence, the estimator can recover the state vector of the system from an under-determined linear set of equations. We use a greedy search algorithm to calculate the sparsifying basis. Then, we present an upper bound for the estimation error. Finally, we demonstrate the results on a numerical example.

#### [C10] Stochastic Sensor Scheduling with Application to Networked Control

F. Farokhi and K. H. Johansson
Conference Papers in Proceedings of American Control Conference (ACC 2013), Washington, DC, USA, June 17-19, 2013.

#### Abstract

We consider stochastic sensor scheduling with application to networked control systems. We model sampling instances (in a networked system) using jumps between states of a continuous-time Markov chain. We introduce a cost function for this Markov chain which is composed of terms depending on the average sampling frequencies of the subsystems and the effort needed for changing the parameters of the underlying Markov chain. By extending Brockett's recent contribution in optimal control of Markov chains, we extract an optimal scheduling policy to fairly allocate network resources (i.e., access to the network) among the control loops. We apply this scheduling policy to a networked control system composed of several scalar decoupled subsystems and compute upper bounds for their closed-loop performance. We illustrate the developed results numerically on a networked system composed of several water tanks.

#### [C9] Complexity Reduction for Parameter-Dependent Linear Systems

F. Farokhi, H. Sandberg, and K. H. Johansson
Conference Papers in Proceedings of American Control Conference (ACC 2013), Washington, DC, USA, June 17-19, 2013.

#### Abstract

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with fewer parameters or state variables. To do so, it minimizes the distance (i.e., H-infinity-norm of the difference) between the original system and its reduced version. We present a sub-optimal solution to this problem using sum-of-squares optimization methods. We present the results for both continuous-time and discrete-time systems. Lastly, we illustrate the applicability of our proposed algorithm on numerical examples.

#### [C8] Limited Model Information Control Design for Linear Discrete-Time Systems with Stochastic Parameters

F. Farokhi and K. H. Johansson
Conference Papers in Proceedings of the 51st IEEE Conference on Decision and Control (CDC 2012), Maui, Hawaii, USA, December 10-13, 2012.

#### Abstract

We design optimal local controllers for interconnected discrete-time linear systems with stochastically varying parameters using exact local model information and statistical beliefs about the model of the rest of the system. We study the value of model information in control design using the closed-loop performance degradation caused by the lack of full model information in the control design procedure. This performance degradation is captured using the ratio of the cost of the optimal controller with limited model information over the cost of the optimal controller with full model information. Both finite-horizon and infinite-horizon cost functions are considered. A numerical example illustrates the developed approach.

#### [C7] Optimal Disturbance Accommodation Design with Limited Model Information

F. Farokhi, C. Langbort, and K. H. Johansson
Conference Papers in Proceedings of American Control Conference (ACC 2012), Montreal, Canada, June 27-29, 2012.

#### Abstract

The design of optimal dynamic disturbance accommodation controller with limited model information is considered. We adapt the family of limited model information control design strategies, defined earlier by the authors, to handle dynamic controllers. This family of limited model information design strategies construct subcontrollers distributively by accessing only local plant model information. The closed-loop performance of the dynamic controllers that they can produce are studied using a performance metric called the competitive ratio which is the worst case ratio of the cost a control design strategy to the cost of the optimal control design with full model information.

#### [C6] On the Value of Model Information in Decentralized Control Design

F. Farokhi, C. Langbort, and K. H. Johansson
Conference Papersin Proceedings of Swedish Control Conference (Reglermöte 2012), Uppsala, Sweden, June 12-14, 2012.

#### Abstract

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods with structured static state feedback controllers, where each subsystem's controller can access at least the state measurement of those subsystems that can affect its corresponding subsystem. We find the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. At last, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

#### [C5] Towards an Indoor Testbed for Mobile Networked Control Systems

M. Larsson, J. Lindberg, J. Lycke, K. Hansson, A. Khakulov, E. Ringh, F. Svensson, I. Tjernberg, A. Alam, J. Araujo, F. Farokhi, E. Ghadimi, A. Teixeira, D. V. Dimarogonas, and K. H. Johansson
Conference Papers in Proceedings of the 1st Workshop on Research, Development, and Education on Unmanned Aerial Systems (RED-UAS 2011), Seville, Spain, November 30-December 1, 2011.

#### Abstract

In this paper, we consider the design of an indoor testbed composed of multiple aerial and ground unmanned vehicles for experimentation in Mobile Networked Control Systems. Taking several mo- tivational aspects from both research and education into account, we propose an architecture to cope with the scale and mobility aspects of the overall system. Currently, the testbed is composed of several low-cost ARdrones quadrotors, small-scale heavy duty vehicles, wireless sensor nodes and a vision-based localization system. As an example, the automatic control of an ARdrone is shown.

#### [C4] Dynamic Control Design Based on Limited Model Information

F. Farokhi and K. H. Johansson
Conference Papers in Proceedings of Annual Allerton Conference on Communication, Control, and Computing (Allerton 2011), Monticello, Illinois, USA, September 28-30, 2011.

#### Abstract

The design of optimal H-2 dynamic controllers for interconnected linear systems using limited plant model information is considered. Control design strategies based on various degrees of model information are compared using the competitive ratio as a performance metric, that is, the worst case control performance for a given design strategy normalized with the optimal control performance based on full model information. An explicit minimizer of the competitive ratio is found. It is shown that this control design strategy is not dominated by any other strategy with the same amount of model information. The result applies to a class of system interconnections and design information characterized through given plant, control, and design graphs.

#### [C3] Control Design with Limited Model Information

F. Farokhi, C. Langbort, and K. H. Johansson
Conference Papers in Proceedings of American Control Conference (ACC 2011), San Francisco, California, USA, June 29-July 1, 2011.

#### Abstract

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. This class generalizes the notion of communication-less control design methods recently introduced by one of the authors, which construct each sub-controller using only local plant model information. We study the trade off between the amount of model information exploited by a control design method and the quality of controllers it can produce. In particular, we quantify the benefit (in terms of the competitive ratio and domination metrics) of giving the control designer access to the global interconnection structure of the plant-to-be-controlled, in addition to local model information.

#### [C2] A Robust Control-Design Method Using Bode's Ideal Transfer Function

F. Farokhi and H. Sandberg
Conference Papers in Proceedings of Mediterranean Conference on Control and Automation (MED 2011), Corfu Island, Greece, June 20-23, 2011.

#### Abstract

We propose a method for designing loop-shaping controllers using Bode's ideal transfer function. Bode's ideal transfer function is introduced using fractional calculus. The ideal loop transfer function is approximated using the first generation CRONE approximation, and then implemented by means of H-infinity optimization followed by closed-loop controller order reduction of the resulting controller. The design method is confirmed to be powerful and robust by simulating on a flexible transmission system.

#### [C1] On Comparison of Numerical Methods to Solve Nonlinear Fractional Order Differential Equations

F. Farokhi, M. Haeri, and M. S. Tavazoei
Conference Papers in Proceedings of Fractional Difference and its Application (FDA 2008), Ankara, Turkey, November 15-17, 2008.

#### Abstract

This paper presents results of comparing some available numerical methods of solving sets of nonlinear fractional order ordinary differential equations. Our study shows that although these methods are easy to implement and accurate enough when are applied to differential equations of fractional order, they have different convergence rate and approximation error. We have compared these methods by their computational complexity, convergence rate, and approximation error.

#### [B2] Distributed MPC Via Dual Decomposition and Alternating Direction Method of Multipliers

F. Farokhi, I. Shames, and K. H. Johansson
Book Chapter in J. M. Maestre and R. R. Negenborn,(Eds.), Distributed Distributed Model Predictive Control Made Easy, Intelligent Systems, Control and Automation: Science and Engineering, 69, Springer, 2013.

#### Abstract

A conventional way to handle model predictive control (MPC) problems distributedly is to solve them via dual decomposition and gradient ascent. However, at each time-step, it might not be feasible to wait for the dual algorithm to converge. As a result, the algorithm might be needed to be terminated prematurely. One is then interested to see if the solution at the point of termination is close to the optimal solution and when one should terminate the algorithm if a certain distance to optimality is to be guaranteed. In this chapter, we look at this problem for distributed systems under general dynamical and performance couplings, then, we make a statement on validity of similar results where the problem is solved using alternative direction method of multipliers.

#### [B1] Comparing Numerical Methods for Solving Nonlinear Fractional Order Differential Equations

F. Farokhi, M. Haeri, and M. S. Tavazoei
Book Chapter in D. Baleanu, Z. B. Guvenc, and J. A. T. Machado, (Eds.), New Trends in Nanotechnology and Fractional Calculus Applications, Springer, 2010.

#### Abstract

This paper is a result of comparison of some available numericalmethods for solving nonlinear fractional order ordinary differential equations. These methods are compared according to their computational complexity, convergence rate, and approximation error. The present study shows that when these methods are applied to nonlinear differential equations of fractional order, they have different convergence rate and approximation error.

#### [M2] Are Route Mapping Apps Truly Private?

F. Farokhi
MediaInterview with The Daily on 2SER, May 24, 2016.

#### Abstract

It is not a surprise to many that most people with smartphones are constantly using various applications every day. Some include privacy features, but what level of privacy do they uphold? WIth the introduction of route mapping apps it's been found that individuals information is becoming readily available for public access.

#### [M1] Protecting Your Privacy If You Use a Route Mapping App

F. Farokhi
MediaThe Conversation, May 16, 2016.

#### Abstract

The first step in preserving our privacy is to understand how much of it we are losing, such as the extent to which privacy-preserving features actually work, and any unintended consequences of their design. In this quest, an important thing that we need to remember is that common sense might not align with reality: privacy zone and anonymisation don’t work, at least not without careful consideration.

#### [T3] Decentralized Control of Networked Systems: Information Asymmetries and Limitations

F. Farokhi
ThesisDoctoral Thesis, 2014, ISBN 978-91-7595-021-1.

#### Abstract

Designing local controllers for networked systems is challenging, because in these systems each local controller can often access only part of the overall information on system parameters and sensor measurements. Traditional control design cannot be easily applied due to the unconventional information patterns, communication network imperfections, and design procedure complexities. How to control large-scale systems is of immediate societal importance as they appear in many emerging applications, such as intelligent transportation systems, smart grids, and energy-efficient buildings. In this thesis, we make three contributions to the problem of designing networked controller under information asymmetries and limitations.

In the first contribution, we investigate how to design local controllers to optimize a cost function using only partial knowledge of the model governing the system. Specifically, we derive some fundamental limitations in the closed-loop performance when the design of each controller only relies on local plant model information. Results are characterized in the structure of the networked system as well as in the available model information. Both deterministic and stochastic formulations are considered for the closed-loop performance and the available information. In the second contribution of the thesis, we study decision making in transportation systems using heterogeneous routing and congestion games. It is shown that a desirable global behavior can emerge from simple local strategies used by the drivers to choose departure times and routes. Finally, the third contribution is a novel stochastic sensor scheduling policy for ad-hoc networked systems, where a varying number of control loops are active at any given time. It is shown that the policy provides stochastic guarantees for the network resources dynamically allocated to each loop.

#### [T2] Decentralized Control Design with Limited Plant Model Information

F. Farokhi
ThesisLicentiate Thesis, 2012, ISBN 978-91-7501-238-4.

#### Abstract

Large-scale control systems are often composed of several smaller interconnected units. For these systems, it is common to employ local controllers, which observe and act locally. At the heart of common control design procedures for distributed systems lies the often implicit assumption that the designer has access to the global plant model information when designing a local controller. However, there are several reasons why such plant model information would not be globally known. One reason could be that the designer wants the parameters of each local controller to only depend on local model information, so that the controllers are not modified if the model parameters of a particular subsystem change. It might also be the case that the design of each local controller is done by individual designers with no access to the global plant model, for instance, due to the fact that the designers refuse to share their model information since they consider it private. This class of problems, which we refer to as limited model information control design, is the topic of the thesis.

First, we investigate the achievable closed-loop performance of discrete-time linear time-invariant plants under a separable quadratic cost performance with structured static state-feedback controllers. To do so, we introduce control design strategies as mappings, which construct controllers by accessing the plant model information in a constrained way according to a given design graph. We compare control design strategies using the competitive ratio as a performance metric, that is, we compare the worst case control performance for a given design strategy normalized with the optimal control performance based on full model information. An explicit minimizer of the competitive ratio is sought. As this minimizer might not be unique, we further search for the ones that are undominated, that is, there is no other control design strategy in the set of limited model information design strategies with a better closed-loop performance for all possible plants while maintaining the same worst-case ratio. We study the trade-off between the amount of model information exploited by a control design strategy and the best possible closed-loop performance. We generalize this setup to structured dynamic state-feedback controllers for H-2 performance. Surprisingly, the optimal control design strategy with limited model information is still a static one. This is the case even though the optimal decentralized state-feedback controller with full model information is dynamic. Finally, we discuss the design of dynamic controllers for disturbance accommodation under limited model information. This problem is of special interest because the best limited model information control design in this case is a dynamic control design strategy. The optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For constant disturbances, it is shown that this structure corresponds to proportional-integral control.

#### [T1] Optimal Design of Partial State-Feedback Controllers

F. Farokhi
ThesisMaster of Science Thesis, 2010. (in Persian)

#### Abstract

Design of optimal controllers for nonlinear systems and even for linear systems is one of the most important parts of the control science. In optimal controller design, our aim is to maximize or minimize some kind of cost function associated with that particular problem. Such cost functions are usually combining the overall control effort, systemís energy, or some other important specifications of the system.

Explicit solution for linear quadratic controllers exists under some mild conditions such as stabilizability of the system. The solution is in the form of a full state-feedback law. But in practical problems, we may not have access to all of the system state variables. The problem can be resolved using a state estimator but such an estimator may compromise the performance and/or the robustness of the closed loop system.

In this presentation, we plan to discuss a method for designing an optimal controller based on a subset of the system state variables or some linear combinations of its states (or outputs). We avoid using a state estimator due to its possible problems. The results of our method are compared to the conventional LQR controller plus state estimator and the advantages and weaknesses are discussed.

At the end we will expand our method to a family of nonlinear systems and will present a method to optimize the feedback linearizing transformation as well as the state-feedback gains.

#### [R3] When Do Potential Functions Exist in Heterogeneous Routing Games?

F. Farokhi, W. Krichene, A. M. Bayen, and K. H. Johansson
Technical ReportTech. Rep. TRITA-EE 2014:009, 2014.

#### Abstract

We study a heterogeneous routing game in which vehicles might belong to more than one type. The type determines the cost of traveling along an edge as a function of the flow of various types of vehicles over that edge. We relax the assumptions needed for the existence of a Nash equilibrium in this heterogeneous routing game. We extend the available results to present necessary and sufficient conditions for the existence of a potential function. We characterize a set of tolls that guarantee the existence of a potential function when only two types of users are participating in the game. We present an upper bound for the price of anarchy (i.e., the worst-case ratio of the social cost calculated for a Nash equilibrium over the social cost for a socially optimal flow) for the case in which only two types of players are participating in a game with affine edge cost functions. A heterogeneous routing game with vehicle platooning incentives is used as an example throughout the article to clarify the concepts and to validate the results.

#### [R2] Decentralized H2 Control Design with Limited Model Information

F. Farokhi, C. Langbort, and K. H. Johansson
Technical ReportTech. Rep. TRITA-EE 2011:064, 2011.

#### Abstract

This paper deals with designing optimal decentralized H2 controller for interconnected discrete-time time-invariant systems with limited model information. We adapt the notion of limited model information designs to handle the dynamic H2 controllers. The best decentralized control design strategy, in terms of the competitive ratio and domination metrics, is found for different acyclic plant graphs when the control graph is a super-graph of the plant graph.

#### [R1] On Designing Optimal Controllers with Limited Model Information

F. Farokhi, C. Langbort, and K. H. Johansson
Technical ReportTech. Rep. TRITA-EE 2010:039, 2010.

#### Abstract

We study a heterogeneous routing game in which vehicles might belong to more than one type. The type determines the cost of traveling along an edge as a function of the flow of various types of vehicles over that edge. We relax the assumptions needed for the existence of a Nash equilibrium in this heterogeneous routing game. We extend the available results to present necessary and sufficient conditions for the existence of a potential function. We characterize a set of tolls that guarantee the existence of a potential function when only two types of users are participating in the game. We present an upper bound for the price of anarchy (i.e., the worst-case ratio of the social cost calculated for a Nash equilibrium over the social cost for a socially optimal flow) for the case in which only two types of players are participating in a game with affine edge cost functions. A heterogeneous routing game with vehicle platooning incentives is used as an example throughout the article to clarify the concepts and to validate the results.

### Teaching History

• 2018

#### Electrical Device Modelling

• Presented 3 guest lectures on vector calculus.

• 2017

#### Secure Cyberphysical Systems

• This subject develops a foundation for pursuing research in the area of secure cyberphysical systems. Issues pertaining to the modelling, detection, and mitigation of attacks in cyberphysical networks are investigated from a system theoretic point of view. The coverage of fundamental material is complemented by exposure to realistic scenarios within the context of small projects.

#### Electrical Device Modelling

• Presented 3 guest lectures on vector calculus.

• 2016

#### Electrical Device Modelling

• Presented 3 guest lectures on vector calculus.

• 2014

#### Introduction to Optimisation

• Presented 1 guest lectures on game theory.

• 2013

#### EL2620 (Nonlinear Control)

• Session 1 (Tuesday, November 5, 2013 at Q36) [notes]

• Session 2 (Thursday, November 7, 2013 at XQ23 and XQ25)

• Session 4 (Thursday, November 15, 2013 at V32) [notes]

• Session 6 (Thursday, November 21, 2013 at Q36) [notes]

• Session 7 (Wednesday, November 27, 2013 at Q36) [notes]

• Session 8 (Monday, December 2, 2013 at Q34) [notes]

• Session 9 (Wednesday, December 4, 2013 at Q31) [notes]

• Session 10 (Friday, December 6, 2013 at XQ23 and XQ25)

• Session 11 (Wednesday, December 11, 2013 at Q33): I was absent and Martin was teaching these sessions.

• Session 12 (Friday, December 13, 2013 at Q34): I was absent and Martin was teaching these sessions.

• Session 13 (Tuesday, December 17, 2013 at Q31) [notes]

• 2012

• 2011

• 2010

### Currrent Students

• 2017

#### A. Zafar

PhD Student, "Developing Efficient Numerical Algorithms for Control of Automated Irrigation Networks", co-supervised with Prof. Michael Cantoni

• 2017

#### A. Saberi

PhD Student, "Fault-Detection with Communication Constraints", co-supervised with Prof. Girish Nair

• 2018

#### C. D. Perera, K. K. Ngo, J. Tran

Capstone Project, ": Sensor and Actuator Interfaces for Encrypted Control", co-supervised with Dr. Iman Shames and Prof. Michael Cantoni

### Former Students

• 2018

#### C. D. Perera, J. Tran, K. Ngo

Capstone Project, "Sensor and Actuator Interfaces for Encrypted Control", co-supervised with Dr. Iman Shames and Prof. Michael Cantoni

2017

#### Q. Li, Z. Li, B. Wu

Capstone Project, "Multi-Quadrotor Co-Ordination", co-supervised with Dr. Iman Shames and Prof. Michael Cantoni

• 2017

#### S. Chen, X. Xiang, W. Gao

Capstone Project, "FPGA Implementation of ADPCM Codec", co-supervised with Dr. Iman Shames and Prof. Michael Cantoni

• 2017

#### A. Shah, F. Hu, K. Zhong

Capstone Project, "FPGA Implementation of MPPT Optimization Algorithm", co-supervised with Dr. Iman Shames and Prof. Michael Cantoni

• 2016

#### P. Zhang, C. Liang, X. Yu

Capstone Project, "Catching a Ball with a Robotic Arm", co-supervised with Dr. Iman Shames

• 2016

#### X. Wang, L. Zou, Z. Sun

Capstone Project, "Heavy-Duty Vehicle Platooning", co-supervised with Prof. Michael Cantoni

• 2016

#### W. Yang, Q. Zhang, Y. Wu

Capstone Project, "Sensing Brain Activities for Robotic Arm Control to Assist People with Disabilities", co-supervised with Dr. Iman Shames

• 2015

#### T. Martin, B. Malandra

Capstone Project, "Sensing Brain Activities for Robotic Arm Control to Assist People with Disabilities", co-supervised with Dr. Iman Shames

• 2015

#### T. Mcnicol, N. Batterham

Capstone Project, "Design, Simulation, and Implementation of Analogue Circuits for Solving Optimization Problems", co-supervised with Dr. Iman Shames

• 2015

#### M. Fasani, G. Maronati

Exchange Master Student, "Sensing Brain Activities for Robotic Arm Control to Assist People with Disabilities", co-supervised with Prof. Michael Cantoni

• 2014

#### M. Biel

ACCESS Summer Project, "Structured ModeL reductIon (SiMpLIfy) Toolbox for MATLAB", co-supervised with Prof. Henrik Sandberg

• 2013

#### E. Hallqvist, S. Håkansson

Bachelor Student, "Networked Control of Autonomous Ground Vehicles"

• 2013

#### A. P. Tellez, J. Roth

Bachelor Student, "Networked Control of Autonomous Ground Vehicles"

• 2012

#### C. Olsson, L. Brandt, T. Axelsson

Bachelor Student, "Detection and Tracking using Wireless UWB and Camera Networks"

• 2012

#### E. Ehrlin, M. Törnqvist

Bachelor Student, "Networked Control of Autonomous Ground Vehicles"

• 2011

#### I. Tjernberg, J. Lindberg, K. Hansson

Bachelor Student, "Cooperative Networked Control of Unmanned Air Vehicles", co-supervised with Dr. Jose Araujo

## My Office at Data61

My office is at Door 34, Goods Shed Village Street Docklands Vic 3008 Australia.

## My Office at the University of Melbourne

My office is at the Control and Signal Processing Laboratory, Level 3, EEE Building (Bldg. 193), University of Melbourne, Parkville, Victoria 3010, Australia.