Memetic Covariance Matrix Adaptation Evolution Strategy for Bilinear Matrix Inequality Problems in Control System Design

TL;DR

This paper introduces a novel memetic CMA-ES algorithm tailored for solving challenging Bilinear Matrix Inequality problems in control system design, demonstrating improved solution quality and robustness.

Contribution

It presents a new integrated memetic CMA-ES approach with local refinement for BMI problems, a novel application in control system optimization.

Findings

Outperforms existing BMI solvers in solution quality

Achieves higher robustness in control design tasks

Effective in $H_{ ext{infty}}$ controller synthesis and spectral abscissa optimization

Abstract

Bilinear Matrix Inequalities (BMIs) are fundamental to control system design but are notoriously difficult to solve due to their nonconvexity. This study addresses BMI-based control optimization problems by adapting and integrating advanced evolutionary strategies. Specifically, a memetic Covariance Matrix Adaptation Evolution Strategy (memetic CMA-ES) is proposed, which incorporates a local refinement phase via a (1+1)-CMA-ES within the global search process. While these algorithmic components are established in evolutionary computing, their tailored integration and specific tuning for control design tasks represent a novel application in this context. Experimental evaluations on $H_{\infty}$ controller synthesis and spectral abscissa optimization demonstrate that the proposed method achieves superior performance compared to existing BMI solvers in terms of both solution quality and robustness. This work bridges the gap between evolutionary computation and control theory, providing a practical and effective approach to tackling challenging BMI-constrained problems.