Optimal Control of Two-Player Systems with Output Feedback

TL;DR

This paper provides a comprehensive solution to the general decentralized two-player optimal control problem with output feedback, extending previous special case solutions and highlighting the coupled estimation and control design.

Contribution

It introduces a detailed method for designing optimal decentralized controllers in the general two-player output feedback setting, including solving coupled estimation and control gains.

Findings

Optimal controllers have a structure similar to centralized controllers.

Coupled estimation and control gains can be computed by solving small linear systems.

The general case lacks the separation principle present in special cases.

Abstract

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.