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

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 2; pp. 442 - 454
• Main Authors: Meng, Deyuan, Moore, Kevin L.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Basic converters; Contraction mapping; Convergence; Ear; Initial conditions; iteration-varying uncertainty; iterative learning control (ILC); Learning; locally Lipschitz condition; Mapping; MIMO (control systems); MIMO communication; Nonlinear dynamical systems; nonlinear system; Nonlinear systems; Nonlinearity; Robots; robust convergence; Robustness; Tracking control; Tracking errors; Trajectory; Uncertainty
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2017.2780131

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.