Adaptive Controller Design for a Class of Uncertain Fractional-Order Nonlinear Systems: An Adaptive Fuzzy Approach

• Published in: International journal of fuzzy systems Vol. 20; no. 2; pp. 366 - 379
• Main Authors: Liu, Heng, Li, Shenggang, Li, Guanjun, Wang, Hongxing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018; Springer Nature B.V
• Subjects: Adaptation; Adaptive systems; Artificial Intelligence; Closed loop systems; Computational Intelligence; Control systems design; Controllers; Design; Differential equations; Engineering; Fuzzy control; Fuzzy logic; Fuzzy sets; Fuzzy systems; Laplace transforms; Liapunov functions; Management Science; Methods; Nonlinear systems; Operations Research; Parameters; Stability analysis; Stability criteria; Fractional-order nonlinear system; Adaptive fuzzy control; Fractional adaptation law
• ISSN: 1562-2479; 2199-3211
• DOI: 10.1007/s40815-017-0371-5

An adaptive fuzzy controller is designed for uncertain fractional-order nonlinear systems in this paper. Fuzzy logic system is utilized to estimate an unknown nonlinear function. By using fractional-order Lyapunov stability criterion, an adaptive fuzzy controller, which is valid for both the Caputo fractional-order systems and the Riemann–Liouville fractional-order systems, is constructed. Fuzzy system parameters are updated by fractional-order differential equations online, and the boundedness of the parameters can be guaranteed. In stability analysis, quadratic Lyapunov functions are utilized, and some basic results which are useful in the stability analysis of fractional-order nonlinear systems are proposed. Finally, simulation results are presented to confirm our results.