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An Introduction to Data Rate Constraints in Feedback Control


u‰‰ŽÒFDr. Girish NairiUniversity of Melbourne, uŽtj
“úŽžF2006”N3ŒŽ7“úi‰Îj13:00`15:00
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u‰‰ŽÒFDr. Girish NairiUniversity of Melbourne, uŽtj

Title: An Introduction to Data Rate Constraints in Feedback Control

Abstract:
In several emerging technologies such as micro-electromechanical systems and sensor networks, the boundary between the fields of communication and control has become blurred. In these applications, the basic aim is to control one or more dynamical systems by feeding back measurements over networks with low data rates. The achievable controller performance can be everely affected by the communication resources available, making it vital to understand how the communication and control objectives interact.

This two-part lecture aims to give an introduction to several recent, fundamental results in the area of networked control. Motivated by the role of Shannon theory in communications, the emphasis is on delineating ultimate bounds, without restriction to specific schemes such as memoryless A-D conversion or linear coders and controllers. In particular, the focus is on characterising the smallest feedback data rate which permits stability to be achieved or some control performance criterion to be met.

In the first part, the case of stochastic linear systems is addressed.
Information and quantisation theory are used to show that in order for bounded mean square states to be possible, the data rate must exceed the intrincis entropy rate of the plant. A universal lower bound on the mean square states is also derived, in terms of data rate and channel delay.
Recent results on the case of bounded states with bounded disturbances will also be discussed, as well as a solution to the problem of optimal LQR under data rate constraints.

Deterministic nonlinear systems are addressed in the second part. It is demonstrated that the classical notion of topological entropy can be extended to yield an intrinsic measure of the smallest rate at which a controlled system can generate information.

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