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

TL;DR

This paper presents a unified method for designing optimal decentralized controllers with current state or output feedback, overcoming coupling issues via reformulation and gradient descent, validated through simulations.

Contribution

It introduces a novel approach to derive and solve the coupled controller gain equations in decentralized control using reformulation and gradient descent.

Findings

Successfully derives explicit controller gain expressions.

Reformulates Riccati equations as forward equations.

Validates method with simulation results.

Abstract

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.