An Information Theoretic Viewpoint to Performance Bounds of Feedback Systems

Nuno Martins, University of Maryland

In this seminar, I will discuss recent results on universal bounds of performance for feedback systems. By using notions from information theory, such as mutual information and (differential) entropy, I characterize conservation laws that hold under causality, which is a basic attribute of physical systems. In particular, I show that the differential entropy, induced by external sources of noise (disturbances), cannot be reduced by feedback. This principle is related to a widely known integral formula, for linear and time-invariant feedback systems, originally derived by Hendrick W. Bode in 1945. The proposed information theoretic viewpoint extends Bode^?s ideas to arbitrary feedback, while providing a suitable framework for considering the case where a finite-horizon preview, of the external noise sources, is available. These results are expressed as bounds, which, holding in great generality, are useful in establishing the optimality of certain feedback schemes.