Design of ℓ1 new suboptimal fractional delays controller for discrete non-minimum phase system under unknown-but-bounded disturbance

Dmitrii Ivanov, Oleg Granichin, Vikentii Pankov, Zeev Volkovich

Research output: Contribution to journalArticlepeer-review

Abstract

1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

Original languageEnglish
Article number69
JournalMathematics
Volume10
Issue number1
DOIs
StatePublished - 1 Jan 2022

Scopus subject areas

  • Mathematics(all)

Keywords

  • Fractional delays
  • Non-minimum phase system
  • Stabilizing controller
  • Unknown-but-bounded noise

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