Data-driven gradient-based point-to-point iterative learning control for nonlinear systems
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ORIGINAL PAPER
Data-driven gradient-based point-to-point iterative learning control for nonlinear systems Benyan Huo · Chris T. Freeman · Yanghong Liu
Received: 25 February 2020 / Accepted: 2 September 2020 © Springer Nature B.V. 2020
Abstract Iterative learning control (ILC) is a wellestablished methodology which has proved successful in achieving accurate tracking control for repeated tasks. However, the majority of ILC algorithms require a nominal plant model and are sensitive to modelling mismatch. This paper focuses on the class of gradientbased ILC algorithms and proposes a data-driven ILC implementation applicable to a general class of nonlinear systems, in which an explicit model of the plant dynamics is not required. The update of the control signal is generated by an additional experiment executed between ILC trials. The framework is further extended by allowing only specific reference points to be tracked, thereby enabling faster convergence. Necessary convergence conditions and corresponding convergence rates for both approaches are derived theoretically. The proposed data-driven approaches are demonstrated through application to a stroke rehabilitation This study was funded by National Natural Science Foundation of China (NO.61473265), the China Postdoctoral Science Foundation (NO.2018M632801) and the ZZU-Southampton Collaborative Research Project under Grant 16306/01. Part of the results in this paper were submitted to 13th IFAC Workshop on Adaptive and Learning Control Systems [1]. B. Huo · Y. Liu (B) School of Electrical Engineering, Zhengzhou University, 100 Science Avenue, Zhengzhou 450001, Henan, China e-mail: [email protected] C. T. Freeman School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK
problem requiring accurate control of nonlinear artificially stimulated muscle dynamics. Keywords Iterative learning control · Data-driven control · Nonlinear systems · Point-to-point tracking · Stroke rehabilitation
1 Introduction Iterative learning control (ILC) is a control paradigm which enables high-performance tracking of tasks which are executed repeatedly over a time interval, each attempt termed a ‘trial’. Distinct from traditional feedback control, standard ILC algorithms can be regarded as implementations of open-loop feedforward control, in which the historical set of tracking error sequences are used to modify the control signal for the next trial [2]. The tracking error over the finite time interval has potential to converge to zero after sufficient trials. Although initially proposed as a model-free approach [3], practical application has been limited by difficulties in tuning control parameters and sensitivity to noise and uncertainty. As a specific class of modelbased ILC, gradient-based algorithms have drawn considerable attention in both theoretical and application domains due to their well-defined convergence and robustness properties [4]. This class includes gradient ILC [5,6], inverse ILC [7] and norm optimal ILC [8,9], which have been app
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