Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM

TL;DR

This paper introduces a convex optimization-based method using symmetric Gauss-Seidel semi-proximal ALM to design decentralized controllers for uncertain systems, ensuring stability and performance with high computational efficiency.

Contribution

It develops a novel convex restriction framework and applies a semi-proximal ALM to efficiently solve the decentralized control problem under uncertainties.

Findings

The method guarantees robust stability and performance.

It achieves high computational efficiency in controller synthesis.

An illustrative example demonstrates the approach's effectiveness.

Abstract

The H2 guaranteed cost decentralized control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational effectiveness. A comprehensive analysis is given on the application of the approach in solving the optimal decentralized control problem; and subsequently, the preserved decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed optimization approach.