A direct adaptive iterative learning control for nonaffine nonlinear discrete-time systems with unknown control directions

In this paper, we propose a direct adaptive iterative learning control for a class of nonaffine nonlinear discrete-time systems with unknown control direction. The fuzzy neural network is firstly used as approximator to compensate for the unknown certainty equivalent controller. Then, in order to solve the uncertainties from approximation errors and random input disturbances, a dead zone like auxiliary error with a time-varying boundary layer is introduced. The auxiliary error is designed for the construction of adaptive laws and the time-varying boundary layer is applied as a bounding parameter. Based on a Lyapunov like analysis, it is shown that the internal signals are bounded and the norm of output tracking error will asymptotically converge to a residual set which is bounded by the width of the boundary layer. Finally, a simulation example is given to verify effectiveness of the proposed direct adaptive iterative learning control.