Iterative learning control for a class of discrete-time singular systems

Panpan Gu,Qian Liu,Senping Tian

doi:10.1186/s13662-018-1471-8

Abstract

This paper is concerned with the iterative learning control problem for a class of discrete-time singular systems. According to the characteristics of the systems, a closed-loop PD-type learning algorithm is proposed and the convergence condition of the algorithm is established. It is shown that the algorithm can guarantee the system output converges to the desired trajectory on the whole time interval. Moreover, the presented algorithm is also suitable for discrete-time singular systems with state delay. Finally, the validity of the presented algorithm is verified by two numerical examples.

Highlights

Iterative learning control (ILC) is an effective control strategy to achieve perfect trajectory tracking for repetitive systems in a finite time interval
4 Extension to systems with state delay we further extend the result of Theorem 1 to a discrete-time singular system with state delay, which is described by
6 Conclusion In this paper, the problem of iterative learning control is investigated for a class of discretetime singular systems

Summary

Introduction

Iterative learning control (ILC) is an effective control strategy to achieve perfect trajectory tracking for repetitive systems in a finite time interval (see [1, 2]). In [16], the ILC technique was applied to a class of singular systems with state delay, the convergence of the algorithm and the possibility of the state tracking were analyzed. Reference [18] applied the ILC strategy to a class of discrete singular systems, the convergence analysis of the algorithm was given in detail by using λ-norm. It should be pointed out that most of the singular systems studied in the above-mentioned works are based on the assumption that the matrix A22 is nonsingular (see [16,17,18]), which implies that the systems are impulse-free (for continue-time singular systems) or causal (for discrete-time singular systems).

Problem description Consider the following discrete-time singular system:

Conclusion