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 excitation, cannot be reduced by feedback. This principle is related to the Bode integral formula, originally derived for linear and time-invariant feedback systems. The aforementioned analysis extends Bode’s ideas to arbitrary feedback, while providing a suitable framework for considering the case where a finite- horizon preview, of the external excitation, is available. In addition, I will describe an information flow inequality that can be used for establishing a universal bound of performance, in the frequency domain. These results are expressed as bounds, which, holding in great generality, are useful in establishing the optimality of certain feedback schemes.
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