Quadratic Optimal Control with Disturbance Attenuation for Uncertain Continuous-Time T-S Fuzzy Systems

ABSTRACT

In this study, an algebraically computational method is proposed to synthesize non-parallel-distributed-compensation (non-PDC) fuzzy controller such that (1) the prescribed disturbance attenuation level for the uncertain continuous-time Takagi-Sugeno (T-S) fuzzy system can be achieved, and (2) a quadratic integral performance index for nominal T-S fuzzy model-based control system can be minimized. We first derive relaxed linear matrix inequality (LMI) conditions by non-quadratic Lyapunov function and non-PDC fuzzy controller to meet prescribed disturbance attenuation level for the uncertain T-S systems. Then by using LMIs and orthogonal function array, the robust quadratic optimal control with disturbance attenuation for uncertain T-S fuzzy system is transformed into constrained-optimization problem represented by algebraic equations and LMI constraints. For static constrained-optimization problem, the HTGA is employed to search the gains non-PDC controllers. Therefore, the robust optimal controller design problem can be greatly simplified with the proposed method. The design example is given to demonstrate the applicability of the proposed approach.

KEYWORDS:

• Disturbance attenuation
• Hybrid Taguchi-genetic algorithm
• Non-quadratic Lyapunov function
• Optimal control
• Orthogonal functions
• Takagi-Sugeno (T-S) fuzzy systems

ACKNOWLEDGMENTS

This work was supported in part by the Ministry of Science and Technology, Taiwan, R.O.C., under Grant Number MOST 105-2221-E-151-024-MY3.

The authors would like to thank the reviewers for their constructive comments and suggestions.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Funding

Ministry of Science and Technology, Taiwan, R.O.C. [grant number MOST 105-2221-E-151-024-MY3].

Notes on contributors

Wen-Ren Horng

Wen-Ren Horng received BS degree from Chung-Yuan Christian University, Chung-Li, Taiwan in 1990 and MS degree from University of Southern California, Los Angeles, U.S.A in 1993, all in Electric Engineering. Now he is working toward his PhD in Department of Electric Engineering at National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan. His research interests are robust control and fuzzy control.

E-mail: [email protected]

Chun-Hsiung Fang

Chun-Hsiung Fang received his diploma from the National Kaohsiung Institute of Technology, Kaohsiung, Taiwan, in 1983, the MS degree from National Taiwan University, Taipei, Taiwan, in 1987, and the PhD degree from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 1997, all in Electrical Engineering. From 1987 to 1990, he served as an instructor of Electrical Engineering Department at National Kaohsiung University of Applied Sciences and was promoted to be an associate professor in 1990. Since 1993, he has been a full professor. From 2008 to 2012, he served as the president of National Kaohsiung University of Applied Sciences. He was a Visiting Scholar at the University of Maryland from 2000 to 2001. Currently, he pays his attention on promoting technology of fitness companies in Xiamen, China. His research interests are in the areas of robust control, singular systems, and fuzzy control.

E-mail: [email protected]

Jyh-Horng Chou

Jyh-Horng Chou received the BS and MS degrees in Engineering Science from National Cheng-Kung University, Tainan, Taiwan, in 1981 and 1983, respectively, and the PhD degree in Mechatronic Engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 1988. He is currently the chair professor of Electrical Engineering Department, National Kaohsiung University of Applied Sciences, Taiwan. He has co-authored four books, and published over 275 refereed journal papers. He also holds six patents. His research and teaching interests include intelligent systems and control, computational intelligence and methods, automation technology, robust control, and robust optimization. He was the recipient of the 2011 Distinguished Research Award from the National Science Council of Taiwan, the 2012 IEEE Outstanding Technical Achievement Award from the IEEE Tainan Section, the 2014 Distinguished Research Award from the Ministry of Science and Technology of Taiwan, the Research Award and the Excellent Research Award from the National Science Council of Taiwan 12 times, and numerous academic awards/honors from various societies. Based on the IEEE Computational Intelligence Society (IEEE CIS) evaluation, his “Industrial Application Success Story” has got the 2014 winner of highest rank, thus being selected to become the first internationally industrial success story being reported on the IEEE CIS website. He is a fellow of the Institute of Electrical and Electronics Engineers (IEEE), the Institution of Engineering and Technology (IET), the Chinese Automatic Control Society (CACS), the Chinese Institute of Automation Engineer (CIAE), and the Chinese Society of Mechanical Engineers (CSME).

E-mail: [email protected]