Robust inversion-based learning control for nonminimum phase systems

This paper introduces a new robust inversion-based learning algorithm for the repetitive tracking control of a class of unstable nonminimum phase systems. After each repetitive trial, the least-squares method is used to estimate the system parameters. The output tracking error and the identified system model are used through stable inversion to find the feed forward input, together with the desired state trajectories, for the next trial. A robust controller is used in each trial to ensure the stability of the systems and the output tracking error convergence. Sufficient conditions for learning control convergence are provided. Simulation studies on the systems with gain uncertainty and time constant uncertainty are also presented. In addition, simulation results demonstrate that the proposed learning control scheme is very effective in reproducing the desired trajectories.