Adaptive Backstepping Fuzzy Control for Nonlinearly Parameterized Systems With Periodic Disturbances

• Published in: IEEE transactions on fuzzy systems Vol. 18; no. 4; pp. 674 - 685
• Main Authors: Chen, Weisheng, Jiao, Licheng, Li, Ruihong, Li, Jing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2010; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive systems; Backstepping; Control systems; Disturbances; Dynamic surface control; Dynamical systems; Educational institutions; Fourier series; Fourier series expansion (FSE); Fuzzy control; Fuzzy systems; fuzzy-logic system (FLS); integral Lyapunov function (ILF); Laboratories; Lyapunov method; Mathematical models; Mathematics; Nonlinear dynamics; nonlinearly parameterized system; periodic disturbance; Programmable control; Tracking errors
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2010.2046329

A novel-function approximator is constructed by combining a fuzzy-logic system with a Fourier series expansion in order to model unknown periodically disturbed system functions. Then, an adaptive backstepping tracking-control scheme is developed, where the dynamic-surface-control approach is used to solve the problem of "explosion of complexity" in the backstepping design procedure, and the time-varying parameter-dependent integral Lyapunov function is used to analyze the stability of the closed-loop system. The semiglobal uniform ultimate boundedness of all closed-loop signals is guaranteed, and the tracking error is proved to converge to a small residual set around the origin. Two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper.