Multi-objective Output Feedback Controller Synthesis using Orthogonal Differential Evolution Algorithm

For multi-objective controller synthesis with H2/H∞ minimization, traditional algorithms try to solve complicated bilinear matrix inequalities; thus, they can only solve low-dimensional problems and have low efficiency. In this study, an improved differential evolution algorithm was developed to solve the multi-objective static output feedback synthesis problem. The orthogonal design method was used to generate the feedback matrix. The H2 and H∞ norms of the closed-loop system were computed, and the locations of the poles were evaluated to determine whether they satisfied the constraints. The differential evolution algorithm was used to search for the optimal value of the objective function. To improve search efficiency, locally enhanced orthogonal crossover operators were introduced into the search process. The proposed algorithm outperformed the traditional algorithm in terms of calculation time and performance index and can be applied to large-scale systems.