Optimal decentralized control of two agent linear system with partial output feedback: certainty equivalence and optimality of linear strategies

摘要

We consider the optimal decentralized control of two agent linear system in which the agent 2's state is affected by the state and control actions of agent 1 but not vice versa. The state of agent 1 is perfectly observed by both agents while the state of agent 2 is observed with noise by agent 2. Thus, the information structure is partially nested. However, we do not assume that the process and observation noises are Gaussian. Therefore, it is not known a priori whether linear strategies are globally optimal. Without using dynamic programming, we show that the optimal strategy is linear and certainty equivalent. Our proof is based on three steps: static reduction via state splitting, orthogonal projection, and completion of squares. We believe that our solution methodology is of independent interest for decentralized control of linear systems.