Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

Abstract

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi–Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

Keywords:

• polynomial fuzzy control
• Takagi–Sugeno fuzzy control
• quantum-inspired evolutionary algorithms
• Lyapunov function
• sum of squares

Additional information

Funding

This work was supported by the National Science Council [grant number NSC 102-2221-E-019-053], [grant number NSC 102-2221-E-194-051].

Notes on contributors

Gwo-Ruey Yu

Gwo-Ruey Yu received the Ph.D. degree in electrical engineering from the University of Southern California, Los Angeles, in 1997. He is currently an Associate Professor of Electrical Engineering Department, National Chung Cheng University, Taiwan. Dr. Yu received the First Prize of the Best Paper Award and the Best Paper Finalist of International Conference on Fuzzy Theory and Its Applications, in 2012 and 2013, respectively. His research interests include quantum information science & technology, intelligent systems and control, and renewable energy systems.

Yu-Chia Huang

Yu-Chia Huang received the B.S. degree in electrical engineering from I-Shou University, Taiwan, in 2007 and the M.S. degree in electrical engineering from National Ilan University, Taiwan, in 2009, where he is currently working toward the Ph.D degree in electrical engineering from National Taiwan Ocean University, Taiwan. His research interests include intelligent systems and control, and nonlinear system control.

Chih-Yung Cheng

Chih-Yung Cheng received the B.S. degree in electrical engineering from National Chiao-Tung University, Taiwan, in 1988, and the M.S. and Ph.D. degrees in electrical engineering from University of Southern California, Los Angeles, in 1990 and 1994, respectively. He is currently an Associate Professor of Electrical Engineering Department, National Taiwan Ocean University, Taiwan. His current research interests include robust control, nonlinear control and intelligent robots.