关键词: 遗传算法(GA), 线性矩阵不等式(LMI), 降阶H∞控制器, 全阶H∞控制器, 实值编码

Abstract: An approach to designing reduced-order H∞ controller for a class of linear continuous dynamic systems is presented based on genetic algorithm. Necessary and sufficient conditions for existence of the controller are given by means of linear matrix inequality. Taking the rank restriction condition as an object function of genetic algorithm, the minimum order nk of the controller and the relevant paired parameter (X,V) of positive definite matrix are obtained by searching the object function globally. Then, the reduced-order H∞ controllers are designed. The genetic algorithm's code is float, the selection operator is rank-based fitness assignment and elitist model, the crossover operator is real valued recombination and the mutation operator is real mutation. The simulation results show that the proposed controller has the same control effect as all-order H∞ controllers based on MATLAB.