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|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)
|Citation:||Regularization Of Hidden Dynamics In Piecewise Smooth Flows. Academic Press Inc Elsevier Science, v. 259, p. 4615-4633 Nov-2015.|
|Appears in Collections:||IMECC - Artigos e Outros Documentos|
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