基于遗传算法的降阶H_∞控制器  

Reduced-Order H_∞ Controllers Based on Genetic Algorithm

作　　者：潘伟[1] 井元伟[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《东北工学院学报》2004年第6期519-522,共4页

基　　金：国家自然科学基金资助项目(69974007);教育部高等学校博士学科点专项科研基金资助项目(20020145007);黑龙江省自然科学基金资助项目(F0318)

摘　　要：考虑一类线性时不变连续动态系统,应用遗传算法给出其降阶H∞控制器的设计方法·用线性矩阵不等式给出控制器存在的充要条件,把秩约束作为遗传算法的目标函数,通过对目标函数的全局搜索,得到控制器的最小阶次nk及相应的正定矩阵参数(X,Y),进而设计出降阶H∞控制器·遗传算法采用实数编码,排序选择和最佳个体保存相结合的选择算子,实值中间重组的交叉算子,实值变异的变异算子·仿真结果表明,所提出方法可达到与MATLAB设计的全阶H∞控制器的相同控制效果,且具有阶次低、易于工程实现的特点·An approach to designing reduced-order H_∞ controller for a class of linear continuous dynamic systems is presented on Genetic Algorithm basis. 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 n_k of the controller and the relevant paired parameter (X,Y) of positive definite matrix are obtained by searching the object function globally. Then, the reduced-order H_∞ controllers are designed. In the genetic algorithm as above the 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.

关 键 词：遗传算法 降阶H∞控制器 线性矩阵不等式 线性时不变连续动态系统 全阶H∞控制器 实值编码 正定矩阵 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]