ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC des...

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Main Authors:	Yong-Hong Lan, Zhe-Min Cui
Format:	Article
Language:	English
Published:	MDPI AG 2018-06-01
Series:	Algorithms
Subjects:	iterative learning control (ILC) fractional order distributed parameter system generalized gronwall inequality
Online Access:	http://www.mdpi.com/1999-4893/11/6/85

id	doaj-845e4ce48c1342a2af0c05f149356734
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spelling	doaj-845e4ce48c1342a2af0c05f1493567342020-11-25T00:40:40ZengMDPI AGAlgorithms1999-48932018-06-011168510.3390/a11060085a11060085ILC with Initial State Learning for Fractional Order Linear Distributed Parameter SystemsYong-Hong Lan0Zhe-Min Cui1School of Information Engineering, Xiangtan University, Xiangtan 411105, ChinaSchool of Information Engineering, Xiangtan University, Xiangtan 411105, ChinaThis paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.http://www.mdpi.com/1999-4893/11/6/85iterative learning control (ILC)fractional orderdistributed parameter systemgeneralized gronwall inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yong-Hong Lan Zhe-Min Cui
spellingShingle	Yong-Hong Lan Zhe-Min Cui ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems Algorithms iterative learning control (ILC) fractional order distributed parameter system generalized gronwall inequality
author_facet	Yong-Hong Lan Zhe-Min Cui
author_sort	Yong-Hong Lan
title	ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
title_short	ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
title_full	ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
title_fullStr	ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
title_full_unstemmed	ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
title_sort	ilc with initial state learning for fractional order linear distributed parameter systems
publisher	MDPI AG
series	Algorithms
issn	1999-4893
publishDate	2018-06-01
description	This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.
topic	iterative learning control (ILC) fractional order distributed parameter system generalized gronwall inequality
url	http://www.mdpi.com/1999-4893/11/6/85
work_keys_str_mv	AT yonghonglan ilcwithinitialstatelearningforfractionalorderlineardistributedparametersystems AT zhemincui ilcwithinitialstatelearningforfractionalorderlineardistributedparametersystems
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ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

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