A Discrete Robust Adaptive Iterative Learning Control for a Class of Nonlinear Systems with Unknown Control Direction

In this paper, a discrete robust adaptive iterative learning control is proposed for a class of uncertain nonlinear systems with unknown control direction and random bounded disturbances. Based on a new design methodology, the problem of unknown sign and upper bound of the time-varying input gain parameter can be solved. In order to deal with the uncertainties from random bounded disturbance and unknown input gain parameter, a dead zone like auxiliary error with a time-varying boundary layer is introduced. This proposed auxiliary error is utilized for the construction of adaptive laws and the time-varying boundary layer is applied as a bounding parameter. By using a Lyapunov like analysis, it is shown that the closed-loop is stable and the internal signals are bounded for all the iterations. Besides, the norm of output tracking error will asymptotically converge to a residual set which is bounded by the width of boundary layer.