Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems

Nanjun Liu, Andrew G Alleyne

Research output: Contribution to journalArticle

Abstract

This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, "Iterative Learning Identification for Linear Time-Varying Systems," IEEE Trans. Control Syst. Technol., 24(1), pp. 310-317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, "A Survey of Iterative Learning Control," IEEE Control Syst. Mag., 26(3), pp. 96-114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.

Original languageEnglish (US)
Article number101003
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Volume138
Issue number10
DOIs
StatePublished - Oct 1 2016

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Time varying systems
learning
Identification (control systems)
Linear systems
linear systems
norms
iteration
Experiments
estimates

Keywords

  • iterative learning control
  • iterative learning identification
  • linear time-varying systems
  • robotics

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications

Cite this

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title = "Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems",
abstract = "This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, {"}Iterative Learning Identification for Linear Time-Varying Systems,{"} IEEE Trans. Control Syst. Technol., 24(1), pp. 310-317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, {"}A Survey of Iterative Learning Control,{"} IEEE Control Syst. Mag., 26(3), pp. 96-114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.",
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