Richard Middleton 
ARC Centre for Complex Dynamic Systems and Control, 
University of Newcastle, Australia

Information Rates and Feedback Control

Abstract:
    
Traditionally in feedback control engineering, there has been a lot of
attention paid to the dynamics and control of important parts of a system,
with comparatively little attention paid to issues related to the
interconnections required to implement feedback control. More recently,
motivated in part by issues in the control of complex systems, there has been
a significant amount of interst in issues to do with information flow,and
communication requirements for feedback control. In this talk I will briefly
discuss some existing results on information rates required for feedback
stabilisation of an unstable system, and also outline some initial results on
links between information flow and performance in feedback systems. In
particular, we will give examples of systems where:

(i) stabilisation demands a minimum information flow
(ii) a specified level of closed loop feedback performance is attainable if
and only if the information flow exceeds a certain required capacity.

References: 

[1] J. H. Braslavsky, R. H. Middleton, and J. S. Freudenberg,
"Feedback stabilization over signal-to-noise ratio constrained channels",
Proceedings of the 2004 American Control Conference, Boston, MA, July 2004,
pp. 4903 * 4908.

[2] "The Minimal Signal-to-Noise Ratio Required to Stabilize over a Noisy
Channel", J. S. Freudenberg, R. H. Middleton, and V. Solo, preprint 2005

[3] G. N. Nair and R. E. Evans, Stabilizability of stochastic linear systems
with finite feedback data rates, SIAM Journal of Control and Optimization,
vol. 43, no. 2, July 2004, pp. 413*436.

[4] T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, 1991.