System identification deals with the problem of building
mathematical models of dynamical systems based on observed data. The
asymptotic properties of system identification methods are well known,
but comparatively little is known about the practical situation where
only a finite number of data points are available. In this project the
finite sample properties of prediction error methods are
considered. Prediction error methods aim at minimising a positive
criterion function of the prediction errors so that the identified
model is the one with the smallest prediction errors. Ideally on would
like to minimise the expected value of the criterion function, but
since the underlying probability measure is unknown, this is not
possible. Instead we employ a prediction error method and minimise the
empirical value of the criterion function evaluated on the observed
data points.
In this project we have derived non-asymptotic bounds on the value of
the criterion function and non-asymptotic confidence ellipsoids for
the parameter estimate. Using these bounds we can compute the number
of data points required in order to guarantee a certain bound with
high probability. So far the results have been obtained using
techniques and methods from learning theory extended to a
dynamical system setting. Currently, we are working towards refining
these results so as to incorporate a-posteriori information (provided
by data).
Water is becoming an increasingly scarce resource world wide, and
modern open channel irrigation systems faces conflicting demands such
as delivering water on short notice and minimum wastage of water. In
this project together with industrial partner Rubicon Systems
Australia Pty, Ltd, we are looking at ways of improving the efficiency
of water delivery using system identification and control techniques.
The water levels and flows are controlled by operating gates which are
located throughout the channel network. As water levels and gate
positions are measured at each gate, large amounts of high quality
data are available for system identification and estimation
purposes. Particular topics addressed in this work include: Estimation
of flow over a gate using level and gate position measurements, System
identification of irrigation channels for prediction and control
purposes, Design of decentralised (monivariable) control systems, Design
of multivariable control systems for irrigation channel networks,
Control under communication constraints and
Fault detection and performance monitoring systems for irrigation
channels.
More information on
CSSIP's webpage.
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