Robust fuzzy control and evolutionary fuzzy identification of singularly perturbed nonlinear systems with parameter uncertainty

• Published in: Electrical engineering 2008-05, Vol.90 (5), p.379-393
• Main Authors: Chang, Yau-Zen, Tsai, Zhi-Ren, Hwang, Jiing-Dong, Lee, Jye
• Format: Article
• Language: English
• Subjects: Economics and Management; Electrical Engineering; Electrical Machines and Networks; Energy Policy; Engineering; Original Paper; Power Electronics
• ISSN: 0948-7921; 1432-0487
• DOI: 10.1007/s00202-007-0085-z

This paper presents an H ∞ robust fuzzy control strategy which stabilizes singularly perturbed (SP) nonlinear systems with bounded uncertainties and guarantees disturbance attenuation bounds for all admissible uncertainties. The modified Takagi–Sugeno (T–S) fuzzy linear models are used to describe the SP nonlinear systems. By the proposed fuzzy control strategy, the number and type of membership functions in the fuzzy control rules are not necessarily the same as those in the fuzzy models. A sufficient condition for the existence of the H ∞ robust fuzzy controllers is then presented in terms of a novel linear matrix inequalities (LMIs) form which takes full consideration of modeling error and uncertainties in system parameters. This condition provides extra design parameters with more flexibility in control gain selection. Furthermore, we propose a compound search strategy composed of island genetic algorithms concatenated with the simplex method to identify the uncertain SP nonlinear systems for the fuzzy control design, and to solve the LMI problem. Finally, design example of the proposed H ∞ robust fuzzy controller for an uncertain SP nonlinear system is presented.