On the Fuzzy Discrete-Time AILC for a Class of Nonlinear MIMO Systems

A fuzzy discrete-time adaptive iterative learning control for a class of uncertain nonlinear discrete-time MIMO systems with random disturbance is proposed in this paper. Since the plant nonlinearity is unknown, a fuzzy system is firstly used as a function approximator to compensate the unknown ideal certainty equivalent controller. Besides, an adaptive time-varying boundary layer is introduced not only to overcome the problem of function approximation error and random disturbance but also to construct an auxiliary error function for the design of adaptive laws. Based on a Lyapunov like analysis, we show that all adjustable parameters as well as the internal signals remain bounded for all iterations and the output tracking error will asymptotically converge to a residual set whose size depends on the width of boundary layer as iteration goes to infinity.