Maxim Raginsky: The limits of control: An information-theoretic viewpoint

Presented February 22nd, 2013 at the University of Florida by the Laboratory for Cognition and Control in Complex Systems.

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Abstract:

Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount importance. In this talk, I consider the general problem of adaptively controlling and/or identifying a stochastic dynamical system, where a priori knowledge allows us to place the system in a subset of a metric space (the uncertainty set). I will present an information-theoretic meta-theorem that captures the trade-off between the metric complexity (or richness) of the uncertainty set, the amount of information acquired online in the process of controlling and observing the system, and the residual uncertainty remaining after the observations have been collected. Following the approach of G. Zames, I quantify a priori information by the Kolmogorov (metric) entropy of the uncertainty set, while the information acquired online is expressed as a sum of information divergences. I will then use the meta-theorem to derive new minimax lower bounds on the metric identification error, as well as to give a simple derivation of the minimum time needed to stabilize an uncertain stochastic linear system.

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