Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/244105
Type: Artigo
Title: Regularization of hidden dynamics in piecewise smooth flows
Author: Novaes, Douglas D.
Jeffrey, Mike R.
Abstract: This paper studies the equivalence between differentiable and non-differentiable dynamics in R-n. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo switches at thresholds in phase space. The canonical convex combination at the discontinuity is only the linear part of a nonlinear combination that more fully explores Filippov's most general problem: the differential inclusion. Here we show how recent work relating discontinuous systems to singular limits of continuous (or regularized) systems extends to nonlinear combinations. We show that if sliding occurs in a discontinuous systems, there exists a differentiable slow fast system with equivalent slow invariant dynamics. We also show the corresponding result for the pinching method, a converse to regularization which approximates a smooth system by a discontinuous one. (C) 2015 Elsevier Inc. All rights reserved.
This paper studies the equivalence between differentiable and non-differentiable dynamics in R-n. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo switches at thres
Subject: Teoria dos sistemas dinâmicos
Filippov, Sistemas de
Campos vetoriais descontínuos
Perturbação singular (Matemática)
Country: Estados Unidos
Editor: Elsevier
Citation: Regularization Of Hidden Dynamics In Piecewise Smooth Flows. Academic Press Inc Elsevier Science, v. 259, p. 4615-4633 Nov-2015.
Rights: Fechado
Identifier DOI: 10.1016/j.jde.2015.06.005
Address: http://www.sciencedirect.com/science/article/pii/S0022039615003083
Date Issue: 2015
Appears in Collections:IMECC - Artigos e Outros Documentos

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