Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach

In this paper, the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single-input single-output (SISO) strict-feedback nonlinear systems with unknown time-delay functions is investigated. Dynamic surface control technique is used to avoid the problem of "explosion of complexity," which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process. In addition, the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions. The designed controller can guarantee all the signals in the closed-loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin. Simulations results are provided to demonstrate the effectiveness of the proposed methods.Qi Zhou, Peng Shi, Shengyuan Xu, and Hongyi L