In this article, we propose a differential evolution (DE) algorithm specifically tailored for the design of linear-quadratic-Gaussian (LQG) controllers in quantum systems. Building upon the foundational DE framework, the algorithm incorporates specialized modules, including relaxed feasibility rules, a scheduled penalty function, adaptive search range adjustment, and the "bet-and-run" initialization strategy. These enhancements improve the algorithm's exploration and exploitation capabilities while addressing the unique physical realizability requirements of quantum systems. The proposed method is applied to a quantum optical system, where three distinct controllers with varying configurations relative to the plant are designed. The resulting controllers demonstrate superior performance, achieving lower LQG performance indices compared to existing approaches. In addition, the algorithm ensures that the designs comply with physical realizability constraints, guaranteeing compatibility with practical quantum platforms. The proposed approach holds significant potential for application to other linear quantum systems in performance optimization tasks subject to physically feasible constraints.
Song et al. (Thu,) studied this question.