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Robust Design of a Class of Time-Delay Iterative Learning Control Systems With Initial Shifts.

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Title: Robust Design of a Class of Time-Delay Iterative Learning Control Systems With Initial Shifts.
Authors: Deyuan Meng1 dymeng23@126.com, Yingmin Jia1,2 ymjia@buaa.edu.cn, Junping Du3 junpingdu@126.com, Fashan Yu4 yufs@hpu.edu.cn
Source: IEEE Transactions on Circuits & Systems. Part I: Regular Papers. Aug2009, Vol. 56 Issue 8, p1744-1757. 14p.
Subjects: Time delay systems, Matrix inequalities, Systems theory, Control theory (Engineering), Feedback control systems, Process control systems
Abstract: This paper is mainly devoted to the iterative learning control (ILC) design for time-delay systems (TDS) in the presence of initial shifts, especially when the system parameters are subject to polytopic-type uncertainties. The ILC laws using a pure error term and/or an initial rectifying action to address the initial shifts are considered, and the two-dimensional (2-D) system theory is employed to develop necessary and sufficient conditions for the asymptotic stability of ILC. For the monotonic convergence of ILC, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) based on the bounded real lemma (BRL). It is shown that adding the pure error term in the D-type learning law helps to meet certain LMIs to achieve a monotonically convergent ILC law. Specifically, this property is first investigated for linear time-invariant systems (LTIS), which is then discussed for the possible extension to TDS. Two numerical examples are included to illustrate the main results. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Circuits & Systems. Part I: Regular Papers is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Robust Design of a Class of Time-Delay Iterative Learning Control Systems With Initial Shifts.
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  Data: <searchLink fieldCode="AR" term="%22Deyuan+Meng%22">Deyuan Meng</searchLink><relatesTo>1</relatesTo><i> dymeng23@126.com</i><br /><searchLink fieldCode="AR" term="%22Yingmin+Jia%22">Yingmin Jia</searchLink><relatesTo>1,2</relatesTo><i> ymjia@buaa.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Junping+Du%22">Junping Du</searchLink><relatesTo>3</relatesTo><i> junpingdu@126.com</i><br /><searchLink fieldCode="AR" term="%22Fashan+Yu%22">Fashan Yu</searchLink><relatesTo>4</relatesTo><i> yufs@hpu.edu.cn</i>
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  Data: <searchLink fieldCode="DE" term="%22Time+delay+systems%22">Time delay systems</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+inequalities%22">Matrix inequalities</searchLink><br /><searchLink fieldCode="DE" term="%22Systems+theory%22">Systems theory</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Process+control+systems%22">Process control systems</searchLink>
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  Data: This paper is mainly devoted to the iterative learning control (ILC) design for time-delay systems (TDS) in the presence of initial shifts, especially when the system parameters are subject to polytopic-type uncertainties. The ILC laws using a pure error term and/or an initial rectifying action to address the initial shifts are considered, and the two-dimensional (2-D) system theory is employed to develop necessary and sufficient conditions for the asymptotic stability of ILC. For the monotonic convergence of ILC, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) based on the bounded real lemma (BRL). It is shown that adding the pure error term in the D-type learning law helps to meet certain LMIs to achieve a monotonically convergent ILC law. Specifically, this property is first investigated for linear time-invariant systems (LTIS), which is then discussed for the possible extension to TDS. Two numerical examples are included to illustrate the main results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IEEE Transactions on Circuits & Systems. Part I: Regular Papers is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1109/TCSI.2008.2010103
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 1744
    Subjects:
      – SubjectFull: Time delay systems
        Type: general
      – SubjectFull: Matrix inequalities
        Type: general
      – SubjectFull: Systems theory
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
      – SubjectFull: Process control systems
        Type: general
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      – TitleFull: Robust Design of a Class of Time-Delay Iterative Learning Control Systems With Initial Shifts.
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            NameFull: Deyuan Meng
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            NameFull: Yingmin Jia
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            NameFull: Junping Du
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            NameFull: Fashan Yu
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              M: 08
              Text: Aug2009
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              Y: 2009
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            – TitleFull: IEEE Transactions on Circuits & Systems. Part I: Regular Papers
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