Iterative learning control based on dynamic time warping for a class of discrete-time nonlinear systems with varying trial lengths and terminus constraint

This paper proposes a dynamic time warping (DTW)-based iterative learning control (ILC) scheme for discrete-time nonlinear systems to tackle the path learning problem with varying trial lengths and terminus constraint. By incorporating the improved DTW algorithm, the varying trial lengths are aligned as a desired length. Meanwhile, this algorithm can find the most similar waypoints between the output and the desired paths, which can be used to design an updating law and facilitate the convergence of path learning. Different from the existing ILC methods based on the probability distribution function for learning trajectory in the time domain, the method in this paper can be applied to learn the spatial path corresponding to the desired trajectory. Furthermore, the learning property in the presence of variable initial states is discussed under the proposed method. Several illustrative examples manifest the validity of the proposed DTW-based ILC algorithm.