Exponential stability of nonlinear differential repetitive processes with applications to iterative learning control

This chapter aims to study the problem of stability analysis, and robust exponential stabilization for a class of switched linear systems with polytopic uncertainties is reviewed. A sufficient condition based on the average dwell time that guarantees the exponential stability of uncertain switched linear systems is given. First, the iterative learning control is presented to build a formulation ensuring the exponential stability of the given system. The integrated design of this ILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. The results are obtained through original connection with the notion of stability along the pass for 2D repetitive systems. An overview of the stabilization methods of switched discrete systems found in the literature is outlined. All the given formulations are presented in terms of LMIs. A numerical simulation example is established, showing the effectiveness of the proposed method.

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Stability of Switched Differential Repetitive Processes and Iterative Learning Control Design

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.1931 ◽

2020 ◽

Vol 53 (2) ◽

pp. 1456-1461

Author(s):

Julia Emelianova ◽

Pavel Pakshin ◽

Mikhail Emelianov

Keyword(s):

Iterative Learning Control ◽

Control Design ◽

Learning Control ◽

Iterative Learning ◽

Repetitive Processes

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An adaptive iterative learning control strategy for discrete repetitive processes with non-repetitiveness in the iteration domain

Proceeding of the 11th World Congress on Intelligent Control and Automation ◽

10.1109/wcica.2014.7053405 ◽

2014 ◽

Author(s):

Jinxue Xu ◽

Xin Du

Keyword(s):

Control Strategy ◽

Iterative Learning Control ◽

Learning Control ◽

Iterative Learning ◽

Adaptive Iterative Learning Control ◽

Repetitive Processes ◽

Discrete Repetitive Processes

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Robust PD-Type Iterative Learning Control of Discrete Linear Repetitive Processes in the Finite Frequency Domain

Mathematics ◽

10.3390/math8061004 ◽

2020 ◽

Vol 8 (6) ◽

pp. 1004

Author(s):

Lei Wang ◽

Mu Li ◽

Huizhong Yang

Keyword(s):

Frequency Domain ◽

Iterative Learning Control ◽

State Feedback ◽

Learning Control ◽

Iterative Learning ◽

Injection Velocity ◽

Linear Matrix ◽

Finite Frequency ◽

Repetitive Processes ◽

Linear Repetitive Processes

This paper studies a robust iterative learning control design for discrete linear repetitive processes in the finite frequency domain. Firstly, the state-space model of the iterative learning process is deduced. Then the dynamic performance condition of the control system in the finite frequency domain is derived by combining it with the stability theory of discrete linear repetitive processes. The system performances in the finite frequency domain are then transformed into the corresponding solutions of the linear matrix inequality by using the generalised KYP lemma. Finally, an integrated state feedback PD-type iterative learning control strategy is proposed. The robust control problem with norm-bounded uncertainty and convex polyhedral uncertainty are also considered in this paper. The simulation of the injection velocity in injection molding verified that the proposed methods in this paper are more effective than the P-type state feedback iterative learning control algorithm.

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