Design of polynomial fuzzy observer-controller with membership functions using unmeasurable premise variables for nonlinear systems

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• 作者：Chuang Liu ; ^a ; ^{chuang.liu@kcl.ac.uk" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; H.K. Lam^a ; ^{hak-keung.lam@kcl.ac.uk" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Xiaojun Ban^b ; ^{banxiaojun@hit.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Xudong Zhao^c ; ^{xdzhaohit@gmail.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Polynomial fuzzy observer&ndash ; controller ; Optimized membership functions ; Unmeasurable premise variables ; Nonlinear system ; Sum of squares (SOS) ; Gradient descent
• 刊名：Information Sciences
• 出版年：2016
• 出版时间：10 August 2016
• 年：2016
• 卷：355-356
• 期：Complete
• 页码：186-207
• 全文大小：2558 K

文摘

In this paper, the stability of polynomial fuzzy-model-based (PFMB) observer-control system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy-model-based (FMB) control strategy, it leads to non-convex stability conditions. Therefore, the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares (SOS) with less manually designed parameters. In addition, the membership functions of the polynomial observer-controller are optimized by the improved gradient descent method, which outperforms the widely applied parallel distributed compensation (PDC) approach according to a general performance index. Simulation examples are provided to verify the proposed design and optimization scheme.