Adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown time delays

A novel adaptive jazzy tracking controller is proposed, for a class of strict-feedback nonlinear time-delay systems with unknown virtual control coefficients. The unknown time delays are compensated for by introducing appropriate Lyapunov-Krasovskii functionals. Fuzzy logic systems in, Mamdani type are used to approximate unknown nonlinear functions. The decoupled backstepping approach is applied, to construct an adaptive fuzzy tracking controller which guarantees semi-global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error to converge to a small neighborhood around the origin. The proposed design scheme contains less adoptive parameters than the existing results and efficiently overcomes the controller singularity problem. Finally, a simulation example is given to demonstrate the effectiveness of the proposed design procedure.