Multivariable nonparametric learning: A robust iterative inversion‐based control approach

Abstract

Learning control enables significant performance improvement for systems by utilizing past data. Typical design methods aim to achieve fast convergence by using prior system knowledge in the form of a parametric model. To ensure that the learning process converges in the presence of model uncertainties, it is essential that robustness is appropriately introduced, which is particularly challenging for multivariable systems. The aim of the present article is to develop an optimization-based design framework for fast and robust learning control for multivariable systems. This is achieved by connecting robust control and nonparametric frequency response function identification, which results in a design approach that enables the synthesis of learning and robustness parameters on a frequency-by-frequency basis. Application to a multivariable benchmark motion system confirms the potential of the developed framework. K E Y W O R D S frequency response methods, learning control, multivariable control systems, robust control, System identification 1 INTRODUCTION Learning control methods can increase the performance of systems by using past operational data. Iterative learning control (ILC), 1,2 repetitive control (RC), 3 and iterative inversion-based control (IIC) 4 have been developed to increase the tracking performance of systems that start each task under identical conditions or that operate continuously in a periodic fashion. 5,6 Examples of high-precision applications whose performance has been enhanced through learning control include nanopositioning devices, 7,8 additive manufacturing machines, 9,10 and industrial printing systems. 11,12 Convergence, usually in terms of signal norms, is an essential aspect of learning and is typically subject to the following requirements. 1,13(§5.1.1) (R1) The learning process converges in a way that is free of poor learning transients and converges relatively fast. (R2) The performance upon convergence is improved. These requirements should hold in the presence of uncertain dynamics and unknown disturbances, 14 since learning control is typically employed to increase the performance in the presence of these unmodeled phenomena. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Frequency Response Function-Based Learning Control: Analysis and Design for Finite-Time Convergence

“…The model set (5) can be obtained through system identification [18], [19]. To ensure convergence despite the FRF uncertainties, the coefficients L(ω k ) are optimized for robust monotonic convergence as follows [12], [19], [20]…”

Optimal iterative learning control design for continuous-time systems with nonidentical trial lengths using alternating projections between multiple sets

“…The first work is widely credited to [1] and sources for the early literature include the survey papers [2,3,4]. Application areas include robotic-assisted biomedical/rehabilitation devices, see, e.g., [5], multi-agent systems [6,7], batch processing [8], and motion control systems [9,10].…”

Robust monotonic convergent iterative learning control design: An LMI‐based method

“…The abovementioned works provide sufficient conditions for robust monotone convergence of ILC algorithms, and the ILC controller that optimizes the robust monotone convergent rate cannot be explicitly derived. The optimal ILC algorithms are proposed in References 18,19. In Reference 18, a necessary and sufficient condition is proposed for the gradient‐based ILC algorithm to be robustly monotonically convergent in time domain.…”

“…In Reference 18, a necessary and sufficient condition is proposed for the gradient‐based ILC algorithm to be robustly monotonically convergent in time domain. Reference 19 studies the problem in frequency domain, and it shows that the optimal convergence rate can be achieved if the learning function is chosen to be the inverse nominal system. Compared with References 18,19, the form of the learning function of this work is more general in the sense that the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.…”