Projects per year
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 language | English |
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Pages (from-to) | 142-168 |
Number of pages | 27 |
Journal | Communications in Nonlinear Science and Numerical Simulation |
Volume | 50 |
Early online date | 24 Feb 2017 |
DOIs | |
Publication status | Published - Sept 2017 |
Research Groups and Themes
- Engineering Mathematics Research Group
Keywords
- Filippov systems
- Utkin equivalent control
- Hysteresis
- Singular perturbations
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Dive into the research topics of 'A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems'. Together they form a unique fingerprint.Projects
- 1 Finished
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When Worlds Collide: the asymptotics of interacting systems (Career Acceleration Fellowship)
Jeffrey, M. R. (Principal Investigator)
1/08/12 → 1/08/16
Project: Research