Suboptimality of decentralized stochastic control and estimation

A stochastic version of suboptimal decentralized control is formulated to study the effects of interactions on performance of systems which are composed of locally optimal subsystems. Turning this approach the other way, we also investigate suboptimality of the decentralized control which arises from the globally optimal control of the overall interconnected system due to the loss of feedback control connections among the subsystems. Various characterizations of suboptimality are given in terms of interconnection and feedback gain matrices. By duality, we derive the suboptimality conditions for decentralized estimation. The separate solutions of control and estimation problems are used to provide a suboptimal decentralized design for incomplete state information. Additional conditions are obtained for robustness and reliability of the interconnected systems synthesized by a suboptimal decentralized control.