Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems

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

4 Citations (Scopus)
458 Downloads (Pure)

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 languageEnglish
Article number103125
Number of pages11
JournalChaos
Volume25
Issue number10
Early online date27 Oct 2015
DOIs
Publication statusPublished - Oct 2015

Fingerprint

Dive into the research topics of 'Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems'. Together they form a unique fingerprint.

Cite this