skip to main content

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

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 what 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 developed 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.
Authors:
 [1]
  1. Engineering Mathematics, University of Bristol, Merchant Venturer's Building, Bristol BS8 1UB (United Kingdom)
Publication Date:
OSTI Identifier:
22482288
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; ATTRACTORS; CONTROL; FUNCTIONS; MITOSIS; NONLINEAR PROBLEMS; RELAYS; SWITCHES