Regularization of hidden dynamics in piecewise smooth flows
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 conv...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:145303 |
| Acceso en línea: | https://ddd.uab.cat/record/145303 https://dx.doi.org/urn:doi:10.1016/j.jde.2015.06.005 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonconvex theory Nonlinear sliding modes Nonsmooth systems Pinching Regularization Singular perturbations Slow-fast system |
| Sumario: | 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. |
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