In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building...In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.展开更多
针对如何实现差分进化算法求解多目标优化问题,提出了一种基于角度邻域的多目标差分进化算法,通过在选择操作中引入弱支配概念,实现了对多目标优化问题的求解.该算法通过计算目标空间中个体与权重向量的夹角来确定每个个体的邻域,并在...针对如何实现差分进化算法求解多目标优化问题,提出了一种基于角度邻域的多目标差分进化算法,通过在选择操作中引入弱支配概念,实现了对多目标优化问题的求解.该算法通过计算目标空间中个体与权重向量的夹角来确定每个个体的邻域,并在此基础上引入了基于角度邻域的变异策略,使个体的变异在邻域内进行,保证进化方向.此外,该算法创建了一个外部存档用来保存进化过程中的非支配解,并定期对外部存档进行维护,大大改善了解集的分布性.大量的数值仿真实验结果表明通过角度确定邻域的方法比通过欧氏距离确定邻域的方法更加有效,算法所得解集的收敛性和分布性也均明显优于基于分解的差分多目标进化算法(multiobjective evolutionary algorithm based on decomposition and differential evolution,MOEA/D–DE)和非支配排序算法Ⅱ(nondominated sorting genetic algorithm II,NSGA).展开更多
基金supported by the National Natural Science Foundation of China (Nos. 61203309, 61104088, 60835004)the Scientific Research Fund of Hunan Provincial Education Department (No. 12B043)+2 种基金the Natural Science Foundation of Hunan Province (No. 10JJ9007)the Industry-University-Research Combination Innovation Platform of Hunan Province (No. 2010XK6066)the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.
基金supported by the Key Project of Chinese Ministry of Education(No.212135)Guangxi Natural Science Foundation(Nos.2012GXNSFB A053165)+2 种基金the Project of Education Department of Guangxi Autonomous Region(Nos.201203YB131,201202ZD071)Doctoral Initiating Project of Guangxi University of Technology(No.11Z09)the Fundamental Research Funds for the Central Universities(No.20112M0126)
文摘针对如何实现差分进化算法求解多目标优化问题,提出了一种基于角度邻域的多目标差分进化算法,通过在选择操作中引入弱支配概念,实现了对多目标优化问题的求解.该算法通过计算目标空间中个体与权重向量的夹角来确定每个个体的邻域,并在此基础上引入了基于角度邻域的变异策略,使个体的变异在邻域内进行,保证进化方向.此外,该算法创建了一个外部存档用来保存进化过程中的非支配解,并定期对外部存档进行维护,大大改善了解集的分布性.大量的数值仿真实验结果表明通过角度确定邻域的方法比通过欧氏距离确定邻域的方法更加有效,算法所得解集的收敛性和分布性也均明显优于基于分解的差分多目标进化算法(multiobjective evolutionary algorithm based on decomposition and differential evolution,MOEA/D–DE)和非支配排序算法Ⅱ(nondominated sorting genetic algorithm II,NSGA).
