A General Method for Optimal Decentralized Control with Current State/Output Feedback Strategy

This paper explores the decentralized control of linear deterministic systems in which different controllers operate based on distinct state information, and extends the findings to the output feedback scenario. Assuming the controllers have a linear state feedback structure, we derive the expression for the controller gain matrices using the matrix maximum principle. This results in an implicit expression that couples the gain matrices with the state. By reformulating the backward Riccati equation as a forward equation, we overcome the coupling between the backward Riccati equation and the forward state equation. Additionally, we employ a gradient descent algorithm to find the solution to the implicit equation. This approach is validated through simulation examples.