Optimal Control Designs for Vector-valued Witsenhausen Counterexample Setups

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.