Optimal decentralized control of a stochastically switched system with local parameter knowledge

This paper considers an optimal decentralized control problem for a linear system with stochastically switched input/output matrices depending on local parameters. These stochastic parameters are assumed independent in time and available instantaneously to the local controller but with a one time step delay to the other. We first solve this problem for the case of a single 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.