Björn Rüffer

Welcome to my homepage! I'm currently a Research Fellow at the University of Melbourne within the Department of Electrical and Electronic Engineering. The address http://bjoern.rueffer.info is intended as a permanent link to this web-page, and should be robust against changes of employer, country, web-hoster etc.

You might occasionally see different spellings of my name: Bjoern Rueffer or Bjorn Ruffer. The first one is officially accepted and should be used when no umlauts are available. The second spelling makes it easier to pronounce my name for English speakers, but it is not preferred in written form.

Contact details | Research interests | Short curriculum vitae | List of publications | Technical blog (external link)

Research Interests

My main area of interest and research is mathematical systems theory and nonlinear automatic control. Of particular interest to me are monotone systems and large-scale systems. But I am also interested in applications raging from logistic processes, autonomous vehicle formations, neural networks, and optical communication systems to iterative algorithms. Currently I am working on applications in optical communications. Below are some more details regarding different kinds of large-scale systems and problems that I am interested in:

Optical communication networks

Modern long-distance digital communication is based on optical fibre links. Better design of optical amplifiers can make communication more resource efficient and reliable, hence cost effective. My interests in this area includes robustness of large-scale networks and propagation of transients.

Iterative algorithms and dynamical systems

Message-passing algorithms are widely used, e.g., in error correction coding (FEC). A popular example is the iterative decoding of LDPC or turbo codes. Message passing algorithms can equivalently be formulated as very high-order dynamical systems. Understanding these kind of systems leads to a better understanding of iterative error correction decoding and may result in design methods for LDPC codes. On the other hand, techniques that are now standard in information theory may lead to interesting counterparts on the dynamical systems theory side.

Neural networks

Artificial neural networks are a scientific approach to emulate what the human brain does. The human brain contains on average approximately 100 billion neurons. Each of them linked to, on average, several thousand other neurons. Understandably, it is a hard task to understand a large-scale network like the human brain. This is one of the aims of neuroscience. Yet, artificial neural networks of smaller size have successfully been used in an ever-growing number of applications, e.g. for pattern recognition, decoding, or automatic control. I am interested in understanding artificial neural networks as approximations of the brain, as it is, after all, a large-scale dynamical system.

Vehicle formation control

An interesting problem is how a group of vehicles (e.g., trucks, planes, or autonomous underwater vehicles (AUVs)) should maintain a prescribed formation while they simultaneously track a given trajectory. This problem becomes increasingly difficult to tackle, if communication between vehicles is limited. Robust decentralized control aims to tackle these obstacles. Yet, there are also fundamental limitations, also known as string instability.

Autonomous control in logistic processes

Autonomous logistic processes can describe supply chains, transportation, shop floor logistics and more. I have investigated systems like this together with my former colleagues of the Collaborative Research Centre 637 at the University of Bremen, Germany.

Input-to-state stability, general small gain theorems, and applications in automatic control

Input-state-stability (ISS) is a stability concept for nonlinear control systems that has been introduced by Eduardo D. Sontag in 1989. Since then it has become one of the main tools in nonlinear control theory. General ISS small gain theorems can be used to prove stability properties of large-scale systems by decomposing them into lower-order systems. One then proves stability properties of the lower-order systems first and then aggregates these results for the composite large-scale system.

Monotone maps and monotone dynamical systems

A monotone map is a function from one partially ordered space into itself that preserves order. Such a map induces a discrete-time dynamical system, which is hence called a monotone system. Monotone systems naturally arise in the context of general small gain theorems. But also several message-passing algorithms give rise to at least partially monotone systems.

A brief curriculum vitae

Björn Rüffer received his Master of Science degree from the Department of Mathematics at the University of Warwick, UK, in 2004. In 2007 he completed his PhD thesis in the area of mathematical systems theory at the Center for Applied and Industrial Mathematics (ZeTeM) within the Department of Mathematics and Computer Science at the University of Bremen, Germany. In Bremen, he was also a member of the Collaborative Research Centre 637 “Autonomous Cooperating Logistic Processes — A paradigm shift and its limitations.” From October 2007 to June 2009 he was a member of the Signal Processing Microelectronics (SPM) group and the School of Electrical Engineering and Computer Science at the University of Newcastle, Australia. Since July 2009 he is with the Department of Electrical and Electronic Engineering at the University of Melbourne, Australia.

Currently, Björn’s Erdös number is 5. His mathematical ancestors can traced here .

List of Publications

Electronic versions of some of my publications and preprints can be found in the publication databases of SPM and SFB637. Others, indicated by a symbol, can be downloaded directly from this web page. Note, however, that there might be minor differences between the published versions and the preprint versions of my papers available here.

Journal papers and book chapters

[25]

Small-gain conditions and the comparison principle.
IEEE Trans. Autom. Control, 2010. Provisionally accepted November 23, 2009.

[24]

Small gain theorems for large scale systems and construction of ISS Lyapunov functions. (with S. N. Dashkovskiy and F. R. Wirth)
SIAM J. Control Optim., 2010. Provisionally accepted September 3, 2009, arXiv:0901.1842.

[23]

Monotone inequalities, dynamical systems, and paths in the positive orthant of Euclidean n-space.
Positivity, 2010. To appear, accepted April 16, 2009, DOI:10.1007/s11117-009-0016-5 .
The original publication is available at www.springerlink.com.

[22]

Local ISS of large-scale interconnections and estimates for stability regions. (with S. N. Dashkovskiy)
Syst. Control Lett., 2010. To appear, accepted February 2, 2010.

[21]

Connection between cooperative positive systems and integral input-to-state stability of large-scale systems. (with C. M. Kellett and S. R. Weller)
Automatica J. IFAC, 2010. To appear, accepted January 26, 2010..

[20]

Comments on ``A multichannel IOS Small Gain Theorem for Systems With Multiple Time-Varying Communication Delays.''. (with R. Sailer and F. R. Wirth)
IEEE Trans. Autom. Control, 2010. Provisionally accepted December 29, 2009.

[19]

Belief Propagation as a Dynamical System: The Linear Case and Open Problems. (with C. M. Kellett, P. M. Dower and S. R. Weller)
IET Control Theory Appl., 2010. To appear, accepted November 12, 2009.

[18]

Routing in dynamischen Netzen. (with H. Rekersbrink, B. Wenning, B. Scholz-Reiter and C. Görg)
Logistik Management 9(1):25–36, 2007.

[17]

Mathematical Models of Autonomous Logistic Processes. (with B. Scholz-Reiter, F. R. Wirth, M. Freitag, S. N. Dashkovskiy, T. Jagalski and C. de Beer)
In: M. Hülsmann and K. Windt (Eds.): Understanding Autonomous Cooperation and Control in Logistics, pp. 121–138, Springer, 2007.

[16]

An ISS small-gain theorem for general networks. (with S. N. Dashkovskiy and F. R. Wirth)
Math. Control Signals Syst. 19(2):93–122, 2007.

Conference articles

[15]

Integral input-to-state stability of interconnected iISS systems by means of a lower-dimensional comparison system. (with C. M. Kellett and S. R. Weller)
In: Proc. Joint 48th IEEE Conf. Decis. Control and 28th Chinese Contr. Conf., Shanghai, P.R.China, pp. 638–643, 2009.

[14]

Stability of interconnections of ISS systems. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. of the SICE 8th Annual Conference on Control Systems, Kyoto, Japan, pp. 52431–52434, 2008.

[13]

Stability of autonomous vehicle formations using an ISS small-gain theorem for networks. (with S. N. Dashkovskiy and F. R. Wirth)
In: PAMM, Special Issue: 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Bremen, Germany, pp. 10911–10912, March, 2008. DOI:10.1002/pamm.200810911.

[12]

Applications of the general Lyapunov ISS small-gain theorem for networks. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 47th IEEE Conf. Decis. Control, Cancun, Mexico, pp. 25–30, December 9–11, 2008.

[11]

Numerical verification of local input-to-state stability for large networks. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 46th IEEE Conf. Decis. Control, New Orleans, LA, USA, pp. 4471–4476, 2007.

[10]

Application of small gain type theorems in logistics of autonomous processes. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 1st Int. Conference Dynamics in Logistics, Bremen, Germany, pp. 359-366, August 28–30, 2007.

[9]

A Lyapunov small-gain theorem for strongly connected networks. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 7th IFAC Symp. Nonlinear Control Systems, Pretoria, South Africa, pp. 283–288, August 22–24, 2007.

[8]

Discrete time monotone systems: Criteria for global asymptotic stability and applications. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 17th Int. Symp. Math. Th. Networks Systems (MTNS), Kyoto, Japan, pp. 89–97, 2006.

[7]

An ISS Lyapunov function for networks of ISS systems. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 17th Int. Symp. Math. Th. Networks Systems (MTNS), Kyoto, Japan, pp. 77–82, 2006.

[6]

Some remarks on the stability of manufacturing logistic networks. Stability margins. (with B. Scholz-Reiter, F. R. Wirth, M. Freitag, S. N. Dashkovskiy, T. Jagalski and C. de Beer)
In: Proc. Int. Scientific Annual Conference on Operations Research, Bremen, Germany, pp. 91–96, 2005.

[5]

A small-gain type stability criterion for large scale networks of ISS systems. (with S. N. Dashkovskiy and F. R. Wirth)
In: Proc. 44th IEEE Conf. Decis. Control and Europ. Contr. Conf., Seville, Spain, pp. 5633–5638, 2005.

Theses and reports

[4]

Implementing the Belief Propagation Algorithm in MATLAB. (with C. M. Kellett)
Technical report, Department of Electrical Engineering and Computer Science, University of Newcastle, Australia, November, 2008.

[3]

Monotone dynamical systems, graphs, and stability of large-scale interconnected systems.
PhD thesis, Universität Bremen, Germany, October, 2007. Available online at [external resource].

[2]

Construction of ISS Lyapunov functions for networks. (with S. N. Dashkovskiy and F. R. Wirth)
Technical report, ZeTeM, Universität Bremen, Germany, July 19th, 2006.

[1]

Multiple Stochastic Integrals and their relations.
Masters thesis, Dept. Mathematics, University of Warwick, UK, 2003.

© Björn Rüffer 2009, 2010
email:
Last modified: Wed Feb 3 10:18:04 CET 2010
Disclaimer: This page, its contents and style, are the responsibility of the author and do not represent the views, policies or opinions of The University of Melbourne.

Dr. Björn Rüffer