Adaptive ILC for a discrete-time nonlinear system with both parametric and non-parametric uncertainties

In this paper, a discrete adaptive ILC is presented for a time-varying nonlinear system with both parametric and nonparametric uncertainties. A novel estimation of parametric and nonparametric uncertainties is constructed just using the past input and output data, and the uncertainties are completely compensated such that the output tracking error is only affected by external disturbance. As a main contribution of this paper, all the discussions are based on the random initial condition and the iteration-varying target trajectories. When the nonlinear function is generalized Lipschitz continuous and the external disturbance is iteration-varying within a bound, the robust property of the proposed adaptive ILC is guaranteed. And when the nonlinear function is standard Lipschitz continuous and the system is free of external disturbance (or the external disturbance is strictly repeatable), the proposed scheme guarantees an almost perfect tracking over the finite time interval.