Optimal Control of Two-Player Systems with Output Feedback
It provides a complete solution to a fundamental decentralized control problem that had only been solved for special cases, enabling optimal control for a broader class of interconnected systems.
The paper solves the general two-player decentralized optimal control problem with output feedback, showing that the optimal controller structure involves state estimation and static control policies, and that computing the coupled gains reduces to solving a small system of linear equations.
In this article, we consider a fundamental decentralized optimal control problem, which we call the two-player problem. Two subsystems are interconnected in a nested information pattern, and output feedback controllers must be designed for each subsystem. Several special cases of this architecture have previously been solved, such as the state-feedback case or the case where the dynamics of both systems are decoupled. In this paper, we present a detailed solution to the general case. The structure of the optimal decentralized controller is reminiscent of that of the optimal centralized controller; each player must estimate the state of the system given their available information and apply static control policies to these estimates to compute the optimal controller. The previously solved cases benefit from a separation between estimation and control which allows one to compute the control and estimation gains separately. This feature is not present in general, and some of the gains must be solved for simultaneously. We show that computing the required coupled estimation and control gains amounts to solving a small system of linear equations.