Linear repetitive learning controls for nonlinear systems by Padé approximants

Abstract

SummaryWe discuss the use of [m,m]‐Padé approximants in the implementation of repetitive learning controls solving the output tracking problem (via output error feedback) in the presence of uncertain periodic reference and/or disturbance signals with known common period. The aim is to address the stability issues concerning those approximants when a linear learning controller—designed through a detailed stability proof (involving the use of a suitable Lyapunov‐like function) and described by a transfer function exhibiting all its poles with negative real part—is to be obtained as well as to evaluate the corresponding closed‐loop performances: robustness (for instance with respect to additive disturbance noises due to unmodeled sensor dynamics) is consequently achieved with improvements in the output tracking errors appearing as the approximation order m increases. Even though the case of any relative degree may be explicitly addressed, in this paper, for the sake of clarity, we restrict our attention to the learning problem for the class of single‐input, single‐output, minimum phase, time‐invariant systems with known relative degree ρ = 2, uncertain parameters and uncertain output‐dependent nonlinearities. Numerical simulation results illustrate the theoretical derivations. Copyright © 2014 John Wiley & Sons, Ltd.