Contraction Mapping-Based Robust Convergence of Iterative Learning Control with Uncertain, Locally Lipschitz Nonlinearity

This paper studies the output tracking control problems for multiple-input, multiple-output (MIMO) locally Lipschitz nonlinear (LLNL) systems subject to iterative operation and uncertain, iteration-varying external disturbances and initial conditions. Under the assumption of a linear, P-type iterative learning control (ILC) update law, a double-dynamics analysis (DDA) approach is proposed to show the convergence of the ILC process in the presence of the locally Lipschitz nonlinearities and iteration-varying uncertainties. The DDA approach results in a contraction mapping-based convergence condition that guarantees both: 1) the boundedness of all system trajectories and 2) the robust convergence of the output tracking error. Further, a basic system relative degree condition is given that provides a necessary and sufficient (NAS) guarantee of the convergence of the ILC process. As a corollary, it is noted that in the absence of iteration-varying uncertainties, the results likewise provide an NAS convergence guarantee for MIMO LLNL systems. The simulations are presented to illustrate the ideas.