Optimal encoder and control strategies in stochastic control subject to rate constraints for channels with memory and feedback
AuthorCharalambous, C. D.
Kourtellaris, C. K.
Hadjicostis, Christoforos N.
SourceProceedings of the IEEE Conference on Decision and Control
Proceedings of the IEEE Conference on Decision and Control
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This paper is concerned with the joint design of encoder/control strategies which minimize a control payoff subject to a rate constraint on the feedback information provided by the system. The control system is described by a conditional distribution, while the rate is described by the directed information of a noisy communication channel. By generalizing the Posterior Matching Scheme (PMS), a scheme that achieves operational capacity, to channels with memory and feedback, the joint optimality of encoder/control strategies is analyzed. A principle of optimality is derived and a dynamic programming equation is obtained, which together describe how the optimal encoder/control strategies should be selected. It is shown that joint optimality separates into an optimal encoder strategy based on the PMS, and a control strategy obtained via the dynamic programming equation. © 2011 IEEE.