Optimal control of a fully decentralized quadratic regulator

In this paper, we consider a fully decentralized control problem with two dynamically decoupled agents. The objective is to design a state-feedback controller for each agent such that a global quadratic cost is minimized. No communication, explicit or implicit, is permitted between the agents. However, the performance of the agents is coupled via the cost function as well as the process noise. We provide an explicit state-space construction of the optimal controllers, showing that the optimal controllers are dynamic, where the number of states depends on the joint covariance matrix of the process noise. The key step is a novel decomposition of the noise covariance matrix, which allows the convex program associated with the controller synthesis to be split into simpler problems and thereby solved.