A fuzzy neural network based adaptive terminal iterative learning control for nonaffine nonlinear discrete-time systems

In this paper, a fuzzy neural network based adaptive terminal iterative learning controller for nonaffine nonlinear discrete-time systems with iteration-varying desired terminal output and random initial output errors. Since it is assumed that only the terminal output is measurable, a terminal output tracking error model is derived to design the adaptive terminal iterative learning controller by using a system input and output algebraic function as well as the differential mean value theorem. Based on a derived terminal output tracking error model, a fuzzy neural network is applied to approximate the unknown desired terminal iterative learning controller and an iteration-varying boundary layer is used to compensate for the corresponding function approximation error. Since the optimal fuzzy neural parameters for a good approximation and the optimal boundary layer for the fuzzy neural approximation error are in general unknown, an auxiliary terminal error function is derived for the design of adaptive laws. Based on a Lyapunov like analysis, we show that the boundedness of control parameters and control input are guaranteed for each iteration. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.