Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone

 In this paper, adaptive dynamic surface control (DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Then, by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing backstepping-based methods. The main advantages of our approach include: 1) for the n-th-order nonlinear systems, only one parameter needs to be adjusted online in the controller design procedure, which reduces the computation burden greatly. Moreover, the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results; 2) the proposed control scheme does not need to know the time delays and their upper bounds. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound, Finally, simulation results demonstrate the effectiveness of the proposed approach.