Design of mixed H-two/H-infinity optimal control systems using multiobjective differential evolution algorithm

• Published in: Journal of control theory and applications Vol. 11; no. 3; pp. 521 - 528
• Main Authors: Wu, Lianghong, Wang, Yaonan, Zhou, Shaowu, Yuan, Xiaofang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2013; Engineering Research Center of Advanced Mining Equipment, Ministry of Education,Hunan University of Science and Technology, Xiangtan Hunan 411201, China%College of Electric and Information Engineering, Hunan University, Changsha Hunan 410082, China
• Subjects: Algorithms; Complexity; Computational Intelligence; Control; Control and Systems Theory; Design engineering; Differential; Engineering; Evolution; H-infinity; H-infinity control; H-two; Mathematical models; Mechatronics; Multiobjective; Norms; Optimization; Parameter; Polytopic; Robotics; self-adaptive; Synthesis; Systems Theory; uncertainties; Parameter self-adaptive; Differential evolution; Mixed H-two/H-infinity control; Multiobjective optimization; Polytopic uncertainties
• ISSN: 1672-6340; 1993-0623
• DOI: 10.1007/s11768-013-1156-5

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.