Multiobjective tracking control design of T-S fuzzy systems: Fuzzy Pareto optimal approach

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• 作者：Bor-Sen Chen ; ^{bschen@ee.nthu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Shih-Ju Ho ^{d9761821@oz.nthu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：H2/H&infin ; H2/H&infin ; tracking control design ; Linear matrix inequality (LMI) ; Multiobjective fuzzy tracking control ; Non-dominating sorting scheme ; Pareto optimal solution ; T&ndash ; S fuzzy control
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：290
• 期：Complete
• 页码：39-55
• 全文大小：714 K

文摘

In this study, a multiobjective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal H₂$H_2$ and H_∞$H_{\infty }$ reference tracking performance simultaneously. First, the Takagi and Sugeno (T–S) fuzzy model is used to represent the nonlinear dynamic system. Then, based on the T–S fuzzy model, multiobjective H₂/H_∞$H_2/H_{\infty }$ tracking control design problem is formulated as a multiobjective problem (MOP) to minimize the H₂$H_2$ tracking error and H_∞$H_{\infty }$ disturbance attenuation level for the fuzzy system at the same time. Since it is not easy to solve this MOP directly, an indirect method is proposed for the multiobjective H₂/H_∞$H_2/H_{\infty }$ tracking control design. Finally, in order to achieve the simultaneous optimization of the MOP, linear matrix inequality (LMI)-based multiobjective evolution algorithm (LMI-based MOEA) is developed based on non-dominating sorting scheme to efficiently search the set of Pareto optimal solutions for the MOP, from which designer can select one design according to his own preference. Further, the multiobjective H₂/H_∞$H_2/H_{\infty }$ fuzzy control design problem based on the weighted sum method is also solved as an alternative choice. Finally, a simulation example of a robotic system is given to illustrate the design procedure and to confirm the robust and optimal tracking performance of the proposed method.