A fuzzy iterative learning control for nonlinear discrete-time systems with unknown control directions

In this paper, we consider the design of adaptive iterative learning control for a class of uncertain nonlinear discrete-time systems with unknown control direction. A new design methodology using two fuzzy systems is presented to deal with the problem of unknown sign and upper bound of the input gain function. The fuzzy systems are used as approximators to compensate for the system unknown nonlinearities. In order to solve the uncertainties from fuzzy approximation errors and random input disturbance, a dead zone like auxiliary error with a time-varying boundary layer is introduced. The auxiliary error is utilized for the construction of adaptive laws and the time-varying boundary layer is applied as a bounding parameter. Based on a Lyapunov like analysis, we show that the closed-loop is stable and the internal signals are bounded for all the iterations. The learning performance is guaranteed in the sense that the norm of output tracking error vector will asymptotically converge to a residual set which is bounded by the width of boundary layer. Finally, an illustrative example is conducted to verify effectiveness of the proposed fuzzy AILC.