Optimal Control Designs for Vector-valued Witsenhausen Counterexample Setups

Abstract

In this work, necessary and sufficient conditions for empirical coordination of vector-valued Witsenhausen counterexample two terminal setups with non-classical information structure are derived. Vector-valued processing allows to involve coding in the design of the control strategies. Optimal characterizations are obtained for the non-causal encoding and causal decoding case as well as causal encoding and non-causal decoding case. Necessary and sufficient conditions are provided for the case with both non-causal encoding and decoding. The feasible set of target distributions can serve as optimization domain for characterizing the optimal average cost, in particular using Witsenhausen's cost function.

Coordination Coding with Causal Decoder for Vector-valued Witsenhausen Counterexample Setups

“…The achievability proof of Theorem 3 is in Appendix A and the converse proof follows from [4,Theorem II.5]. In order to characterize the set of achievable Witsenhausen costs (P, S), we consider a fixed parameter P ≥ 0 and we minimize…”

“…[3]. A comprehensive overview on the corresponding results is provided in [4], where we also discuss its close relation to the coordination problem. Optimal coding schemes for relevant setups are derived in [5], which also provides a review on the related literature.…”