Title: On Optimization of Information Channels in Stochastic Control (1 hour)
Abstract: We consider the optimization of information channels in stochastic control and estimation problems. First, we discuss structural and topological properties of such channels. Toward this end, we find conditions for continuity of optimal costs on the space communication channels; where setwise and weak convergences of probability measures are used to define such spaces. Furthermore, existence of optimal channels is discussed, and concavity properties of the optimal cost with regard to the channels is presented when the cost functions are convex. Applications of these findings in optimal vector quantizer design, empirical controller design and robust control will be discussed. We then consider the design of a special class of information channels, quantizers, for linear control systems. We find stabilizing quantization and control policies for unstable sources over discrete erasure channels. One by-product of our analysis is a new criterion for verifying stochastic stabilization of Markov chains which satisfy random-time state-dependent drift conditions (thus, extending Meyn and Tweedie's related deterministic-time criteria).