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Distributed Optimal Control over Bit-rate Constrained Networks with Communication delay

In this paper we address the problem of optimal co-design of control and quantization policies for a physically-interconnected system, where each subsystem has a local quantizer. The controllers are assumed to communicate with delay and cooperate in minimizing global quadratic cost. We show that for quantizers that act on the estimation error of the estimator conditioned on common information between controllers, separation holds. In other words, both quantizers can be optimally designed by minimizing a distortion function that is control-independent. Finally, for general class of quantizers we provide structural properties of the optimal control policy.