A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems

Carles Bonet, Tere M. Seara, Enric Fossas, Mike R. Jeffrey

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
240 Downloads (Pure)

Abstract

Abstract Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should the dynamics be given by a limiting value on one side or other of the discontinuity, or a member of some set containing those values? One way to remove the ambiguity is to regularize the discontinuity, the most common being either to smooth it out, or to introduce a hysteresis between switching in one direction or the other across it. Here we show that the two can in general lead to qualitatively different dynamical outcomes. We then define a higher dimensional model with both smoothing and hysteresis, and study the competing limits in which hysteretic or smoothing effects dominate the behaviour, only the former of which correspond to Filippov’s standard ‘sliding modes’.
Original languageEnglish
Pages (from-to)142-168
Number of pages27
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume50
Early online date24 Feb 2017
DOIs
Publication statusPublished - Sep 2017

Keywords

  • Filippov systems
  • Utkin equivalent control
  • Hysteresis
  • Singular perturbations

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