Contraction Analysis of Nonlinear Iterative Learning Control

被引：3
作者：
Kong, Felix H. [1 ]
Manchester, Ian R. [1 ]
机构：
[1] Univ Sydney, Australian Ctr Field Robot, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW, Australia
来源：
IFAC PAPERSONLINE | 2017年 / 50卷 / 01期
关键词：
iterative learning control; contraction analysis; linear matrix inequalities; REPETITIVE CONTROL; SYSTEMS; ILC; STABILITY; DISTURBANCES; ROBUSTNESS; DESIGN; ROBOTS; TIME;
D O I：
10.1016/j.ifacol.2017.08.2444
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Iterative learning control (ILC) is widely used as a simple method for precise tracking of systems under repetitive conditions. ILC operates by "learning" from the previous iteration's errors, correcting them over a number of iterations. However, the question of whether or not a nonlinear ILC system converges is still in general an open one. Assuming a state-space formulation, we use contraction analysis to formulate a convergence condition for ILC system as a linear matrix inequality (LMI). Finally, we compute a convergence certificate for a simple example involving "anticogging" a permanent-magnet synchronous motor driving a pendulum in simulation. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
引用
收藏
页码：10876 / 10881
页数：6
相关论文
共 29 条
[1]   ITERATIVE LEARNING CONTROL FOR A CLASS OF NONLINEAR-SYSTEMS [J].
AHN, HS ;
CHOI, CH ;
KIM, KB .
AUTOMATICA, 1993, 29 (06) :1575-1578
[2]   Iterative learning control: Brief survey and categorization [J].
Ahn, Hyo-Sung ;
Chen, YangQuan ;
Moore, Kevin L. .
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART C-APPLICATIONS AND REVIEWS, 2007, 37 (06) :1099-1121
[3]   BETTERING OPERATION OF ROBOTS BY LEARNING [J].
ARIMOTO, S ;
KAWAMURA, S ;
MIYAZAKI, F .
JOURNAL OF ROBOTIC SYSTEMS, 1984, 1 (02) :123-140
[4]   Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming [J].
Aylward, Erin M. ;
Parrilo, Pablo A. ;
Slotine, Jean-Jacques E. .
AUTOMATICA, 2008, 44 (08) :2163-2170
[5]   A Norm Optimal Approach to Time-Varying ILC With Application to a Multi-Axis Robotic Testbed [J].
Barton, Kira L. ;
Alleyne, Andrew G. .
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, 2011, 19 (01) :166-180
[6]  
Blanken L., 2016, RATIONAL ITERATIVE F, P2629
[7]   A survey of iterative learning control [J].
Bristow, Douglas A. ;
Tharayil, Marina ;
Alleyne, Andrew G. .
IEEE CONTROL SYSTEMS MAGAZINE, 2006, 26 (03) :96-114
[8]   The weighted incremental norm approach:: from linear to nonlinear H∞ control [J].
Fromion, V ;
Monaco, S ;
Normand-Cyrot, D .
AUTOMATICA, 2001, 37 (10) :1585-1592
[9]   LMIs - A fundamental tool in analysis and controller design for discrete linear repetitive processes [J].
Galkowski, K ;
Rogers, E ;
Xu, S ;
Lam, J ;
Owens, DH .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2002, 49 (06) :768-778
[10]   On the design of ILC algorithms using optimization [J].
Gunnarsson, S ;
Norrlöf, M .
AUTOMATICA, 2001, 37 (12) :2011-2016
123