TS-CMAC Based Sliding Mode Control for Time-delay Systems

This paper investigates the problem of sliding mode adaptive TS-CMAC control for a class of nonlinear system with time delay via LMI approach. The nth-order system is not Isidori-Bynes canonical form, so we develop a different way to design the sliding surface and reaching law. First, a novel sliding surface design method is proposed based on Lyapunov-Krasoviskii method. Linear Inequality Matrix (LMI) technique provide to design sliding surface. Second, a new structure of TS-CMAC is proposed to design an adaptive reaching law. The corresponding adaptive reaching law is constructed based on Lyapunov method, which can drive the state trajectory of the close system onto the sliding surface within limited time. In addition, on-line adaptive laws of the control system are derived based on the Lyapunov stability theorem and gradient descent method. Simulation results demonstrate the effective of the proposed control scheme for nonlinear time-delay system with unknown uncertainties.