Robust Data-Driven Iterative Learning Control for Linear-Time-Invariant and Hammerstein-Wiener Systems

• Published in: IEEE transactions on cybernetics Vol. 53; no. 2; pp. 1144 - 1157
• Main Author: Dong, Jianfei
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loops; Control systems; Convergence; Covariance matrices; Data-driven control; Errors; Hammerstein–Wiener (H-W) systems; Hidden Markov models; iterative learning control (ILC); Iterative methods; Learning; Linear systems; Parameter identification; Predictive models; Robust control; robust monotonic convergence (RMC); Uncertainty
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3105745

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.