An Explicit Solution for Optimal Two-Player Decentralized Control over a TCP Erasure Channel with State Feedback

We develop an optimal controller synthesis algorithm for decentralized control problems where control actions are transmitted through TCP-like erasure channels. We consider a simple two-player interconnected linear system and Bernoulli distributed erasure channels. We recast the problem to a centralized Partially Observed Markov Decision Process (POMDP) under the fictitious player framework, in which we construct an optimal controller using belief states and value function recursions. Finally, we provide explicit state space formulae for the optimal decentralized controller.