Unified iterative learning control schemes for nonlinear dynamic systems with nonlinear input uncertainties

In many ILC algorithms, nonlinear input uncertainties such as saturation, dead-zone and hysteresis, which do exist due to practical implementations, are always ignored. Although various ILC algorithms have been proposed to compensate various nonlinear input uncertainties, a systematic design framework is still missing. This note presents a unified design framework to deal with very general nonlinear input uncertainties. The concept of a dual-loop ILC is introduced. One ILC loop (ILC Loop 1) is designed for the nominal model without nonlinear input uncertainties. The other ILC loop (ILC Loop 2) uses some iterative algorithms to handle nonlinear input uncertainties. Two ILC loops can be designed independently and are connected by a proper time-scale separation. Our first result shows that by using time-scale separation, the overall system semi-globally practically converges to the desired trajectory if ILC Loop 2 uniformly converges. Furthermore, if ILC Loop 2 converges “almost” monotonically, ILC Loop 1 and ILC Loop 2 can update simultaneously to achieve uniform convergence of the overall system.