Projects per year
Abstract
Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and that can be retained, when we model a switch as an instantaneous event, requires a consideration of so-called hidden terms. These are asymptotically vanishing outside the switch, but can be encoded in the form of nonlinear switching terms. A general expression for the switch can be eveloped in the form of a series of sigmoid functions. We review the key steps in extending Filippov’s method of sliding modes to such systems. We show how even slight nonlinear effects can hugely alter the behaviour of an electronic control circuit, and lead to ‘hidden’ attractors inside the switching surface.
Original language | English |
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Article number | 103125 |
Number of pages | 11 |
Journal | Chaos |
Volume | 25 |
Issue number | 10 |
Early online date | 27 Oct 2015 |
DOIs | |
Publication status | Published - Oct 2015 |
Research Groups and Themes
- Engineering Mathematics Research Group
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Dive into the research topics of 'Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth 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