A team theoretic approach to decentralized control of systems with stochastic parameters

This paper investigates an optimal decentralized control problem for a system with B-matrices dependent on stochastic parameters. It is assumed that these parameters are independent in time and available locally to each controller. The objective is to find a decentralized state feedback control policy that minimizes a multi step quadratic cost function. We first solve this problem for the case of one time step and show that the optimal policy can be reached through iterating the best responses of each player. For the optimal multiple step problem, a dynamic programming approach is employed while using the result of the one step control at each step. Finally in the infinite horizon case, we provide sufficient conditions under which the optimal control policy is unique and stabilizes the system in a mean square sense.