An adaptive iterative learning control for discrete-time nonlinear systems with iteration-varying uncertainties

In this paper, we present a new adaptive iterative learning controller for a class of discrete-time nonlinear systems with iteration-varying uncertainties including initial tracking error, system parameters and external disturbance. The learning objective is to control the nonlinear system to track an iteration-varying desired trajectory after suitable numbers of learning iterations. The main challenge for the iterative learning control design is that all the system parameters are iteration-varying. After separating the system parameters into a pure time-varying component and an iteration-varying component, the system dynamics are divided into an iteration-independent nominal part and an iteration-dependent uncertain part. An adaptive iterative learning controller is then designed to control the nominal dynamics and an iteration-varying boundary layer with dead-zone like auxiliary error is proposed to compensate for the iteration-varying uncertainties. The control parameters and the width of boundary layer are updated from trial to trial in order to guarantee the stability and convergence of the learning system. In addition to ensure the boundedness of control signals for each iteration and each time instant, we also prove that the norm of output error will asymptotically converge to a residual set whose size depends on the width of boundary layer as iteration number goes to infinity.