Accelerated Iterative Learning Control for Linear Discrete Time Invariant Switched Systems

Yongping Wang,Ziyun Bao,Wenqian Zhang,Saleem Riaz

doi:10.1155/2022/5738826

Abstract

For a class of linear discrete time invariant stochastic switched systems with repetitive operation characteristics, a novel P-type accelerated iterative learning control algorithm with association correction is proposed. Firstly, the concrete form of accelerated learning law is given, and the generation of correction in the algorithm is explained in detail; secondly, on the premise that the switching sequence does not change along the iteration axis but only along the time axis, the convergence of the algorithm is strictly mathematically proved by using the super vector method, and the sufficient conditions for the convergence of the algorithm are given; finally, the theoretical results show that the convergence speed mainly depends on the controlled object, the proportional gain of the control law, the switching sequence, the correction coefficient, the association factor, and the size of the learning interval. Simulation results show that the proposed algorithm has a faster convergence speed than the traditional open-loop P-type algorithm under the same conditions.

Highlights

In recent years, switching system has gradually become one of the research hotspots in the control field [1]
A large number of research results on switched systems are focused on the stability of switched systems [6], but the research results on the output tracking control of switched systems are very limited [7]. e reason is that it is much more difficult to realize the tracking control of switched systems than the stabilization and stability problems [8,9]
It is worth noting that the ILC algorithm and its optimal robust control [10]can be used in many industrial applications such as robotics control [11], industrial automation [12], power and energy sectors [13,14,15], chemical plant processing [16], servo control [17], and many other automation industries [18]

Summary

Introduction

In recent years, switching system has gradually become one of the research hotspots in the control field [1]. Xu-Hui et al [28] proposed an open-loop P-type iterative learning control algorithm for a class of linear discrete stochastic switched systems on the premise that the switching sequence is randomly determined and analyzed the convergence of the algorithm by using the super vector method, realizing the complete tracking of the desired trajectory in the whole running finite time interval. Based on the above analysis, for a class of discrete time invariant arbitrary switching systems that perform repeated tracking tasks on the desired trajectory in a finite time interval, under the premise that the switching sequence is randomly determined and the iteration is unchanged, using the characteristics of iterative learning control, taking p-type as an example, a discrete iterative learning control algorithm with backward error association and correction of the control quantity of the iterative learning is proposed. Combined with the theory of super vector and spectral radius, the convergence of the algorithm is discussed, and sufficient conditions for the convergence of the algorithm are given in theory

Problem Formulation

Convergence Analysis

Numerical Simulation

Conclusions