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            <title xml:lang="en">Optimal Control Designs for Vector-valued Witsenhausen Counterexample Setups</title>
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                <title xml:lang="en">Optimal Control Designs for Vector-valued Witsenhausen Counterexample Setups</title>
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                <term xml:lang="en">empirical coor- dination</term>
                <term xml:lang="en">Witsenhausen counterexample</term>
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              <p>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.</p>
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