The phenomenon of apparent convergence followed by divergence in learning and repetitive control

Richard W. Longman, Yi Cheng Huang

Research output: Contribution to journalArticle

36 Citations (Scopus)


It is a common experimental experience with learning and repetitive control, that the error decreases very substantially in the fast few repetitions or periods, and then starts to grow. In some cases this takes the form of a long term instability, for example in experiments cited here instability became evident only after 2,500 repetitions. Here we develop both time domain and frequency domain approaches to both learning and repetitive control, including use of root locus and Nyquist concepts. And these different viewpoints are used to explain in different ways this phenomenon of apparent initial convergence followed by divergence. It is seen that with typical distributions of tracking errors in the frequency spectrum relative to the bandwidth of the feedback controller, this phenomenon is easily generated. Three classes of approaches aze summarized for addressing this problem, either by stopping the mechanism of divergence, or by causing the convergence to continue to zero tracking error.

Original languageEnglish
Pages (from-to)107-128
Number of pages22
JournalIntelligent Automation and Soft Computing
Issue number2
Publication statusPublished - 2002 Jan 1


All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Artificial Intelligence

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