Decentralized control with noisy transmission of information

We consider an example for a decentralized stochastic optimal control problem, where the non-classical nature of the information pattern is induced by the transmission noise in the system. This example is a reformulation of the Witsenhausen (1968) counterexample, where the first station is allowed to send its information to the second station through an additive white Gaussian noise channel. We establish the nonconvexity of the problem in this new formulation and show that the problem considered here converges asymptotically to the classical problem or the Witsenhausen problem, as the transmission noise intensity converges to zero or diverges to infinity, respectively