Regularization of hidden dynamics in piecewise smooth flows

Autor(es)

Novaes, Douglas D. ^[1] ; Jeffrey, Mike R. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Bristol, Dept Engn Math, Bristol BS8 1UB, Avon - England

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 259, n. 9, p. 4615-4633, NOV 5 2015.
• Citações Web of Science: 10

Resumo

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. (AU)

• Processo FAPESP: 12/10231-7 - Regularização e conjuntos minimais para sistemas dinâmicos não suaves
• Beneficiário: Douglas Duarte Novaes
• Modalidade de apoio: Bolsas no Brasil - Doutorado