Establishing improved convergence and robustness properties for the repetitive learning control

A novel learning control scheme is designed for a class of nonlinear systems. Not only global asymptotic tracking is achieved but also sufficient conditions for the asymptotic “input learning” are derived. The robustness with respect to a finite memory implementation of the control algorithm (which is based on the piecewise linear approximation theory) is guaranteed in the closed loop. The proposed approach allows for the solution of global output tracking problems: (i) for relative degree one systems with output dependent uncertainties; (ii) for nonlinear systems with matching uncertainties.