Regularization of hidden dynamics in piecewise smooth flows
Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática)
Jeffrey, Mike R. (University of Bristol. Department of Engineering Mathematics)

Date:	2015
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.
Note:	Agraïments: M.R.J. is supported by EPSRC grant EP/J001317/2. D.D.N. is supported by a FAPESP-BRAZIL grant 2012/10231-7.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nonconvex theory ; Nonlinear sliding modes ; Nonsmooth systems ; Pinching ; Regularization ; Singular perturbations ; Slow-fast system
Published in:	Journal of differential equations, Vol. 259 (2015) , p. 4615-4633, ISSN 1090-2732

DOI: 10.1016/j.jde.2015.06.005

Postprint 20 p, 399.1 KB

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