Convergence Analysis of Sampled-Data ILC for Locally Lipschitz Continuous Nonlinear Nonaffine Systems With Nonrepetitive Uncertainties

• Published in: IEEE transactions on automatic control Vol. 66; no. 7; pp. 3347 - 3354
• Main Authors: Chi, Ronghu, Hui, Yu, Chien, Chiang-Ju, Huang, Biao, Hou, Zhongsheng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Analytical models; Continuous time systems; Convergence; Data analysis; Iterative methods; Locally Lipschitz continuous (LLC); Machine learning; nonaffine nonlinear continuous-time systems; Nonlinear systems; robust convergence analysis; Robustness; Robustness (mathematics); sampled-data iterative learning control (ILC); Sampling; Tracking errors; Trajectory; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3020803

This article investigates a challenging open problem of convergence analysis of sampled-data iterative learning control for locally Lipschitz continuous (LLC) nonlinear nonaffine continuous-time systems. The restrictive repetitive conditions are relaxed by taking the LLC nonlinear nonaffine systems with iteratively variant initial states, reference trajectories, and exogenous disturbances into consideration. A new convergence analysis method is proposed by incorporating the mathematical induction with the contraction mapping principle (MI-CMP) to prove the boundedness of system variables, and bounded convergence of tracking error for a finite iteration as the first step. Then, the mathematical proof by contradiction is utilized along with the MI-CMP to further prove the robust convergence of the tracking error in any iteration to an error bound related to the bounds of the iteration-varying uncertainties and the sampling period. It is also shown that the tracking error converges to a smaller bound if the iteration-varying uncertainties disappear, even to zero if the sampling period approaches zero. In addition, an algorithm is provided to optimize the learning operator under the convergence condition. Theoretical results are further verified by simulations.