Adaptive Backstepping Fuzzy Control for Nonlinearly Parameterized Systems With Periodic Disturbances
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.
nonlinearly parameterized system periodic disturbance dynamic surface control fourier series expansion (fse) fuzzy-logic system (fls) integral lyapunov function (ilf)