An improved fast error convergence topology for PDα-type fractional-order ILC

Saleem Riaz, Hui Lin, Minhas Mahsud, Deeba Afzal, Ammar Alsinai, Murat Cancan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The monotonic convergence of the PDα-type fractional-order iterative learning control algorithm is considered for a class of fractional-order linear systems. First, a theoretical analysis of the monotonic convergence of 1st and 2nd order PDα-type control algorithms is carried out in the typical terms of Lebesgue-p (Lp), and the sufficient conditions for their monotonic convergence are comprehended and extended to the case of N-order control algorithms; then the speed of convergence of the two is explained in detail. It is concluded that the conditions for convergence of the control algorithm are determined by the learning gain and the system’s properties are together determined. Simulation experiment verifies the accuracy of proposed scheme and the validity of the control algorithm.
Original languageEnglish
Pages (from-to)2005-2019
Number of pages15
JournalJournal of Interdisciplinary Mathematics
Volume24, 2021
Issue number7
Early online date7 Nov 2021
Publication statusPublished online - 7 Nov 2021


  • Iterative learning control (ILC)
  • Fractional-order ILC
  • Lebesgue-p (Lp) norm
  • Error convergence


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