Minimum variation solutions for sliding vector fields on the intersection of two surfaces in \(\mathbb{R}^3\)
type: Item
instance of: scholarly article
title: Minimum variation solutions for sliding vector fields on the intersection of two surfaces in \(\mathbb{R}^3\)
zbMATH Open document ID: 1335.34035
published in: Journal of Computational and Applied Mathematics
publication date: 2015-09-09T00:00:00Z
review text: Te authors consider model problems of piecewise smooth systems in \(\mathbb{R}^3\) and propose minimum variation approaches to find a Filippov sliding vector field on the intersection \(\Sigma\) of two discontinuity surfaces. Their idea is to look at the minimum variation solution in the \(H^1-\)norm, among either all admissible sets of coefficients for a Filippov vector field, or among all Filippov vector fields. They compare the resulting solutions to other possible Filippov sliding vector fields (including the bilinear and moments solutions). The authors further show that -- in the absence of equilibria -- also these other techniques select a minimum variation solution, for an appropriately weighted \(H^1-\)norm, and relate this weight to the change of the time variable giving orbital equivalence among the different vector fields. Finally, they give details of how to build a minimum variation solution for a general piecewise smooth system in \(\mathbb{R}^3\).
reviewed by: Andrej V. Plotnikov
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 65P99
zbMATH DE Number: 6479591
zbMATH Keywords: Filippov sliding motion
zbMATH Keywords: minimum variation solution
author: Luca Dieci
author: Fabio V. Difonzo
MaRDI profile type: Publication
full work available at URL: j.cam.2015.02.026
OpenAlex ID: W1977677836
cites work: Q3994508
cites work: Piecewise-smooth dynamical systems. Theory and applications
cites work: A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis
cites work: Numerical methods for nonsmooth dynamical systems. Applications in mechanics and electronics
cites work: A comparison of Filippov sliding vector fields in codimension 2
cites work: Q4400449
cites work: Q5440982
cites work: A path integral approach to random motion with nonlinear friction
cites work: Sliding motion on the intersection of two manifolds: spirally attractive case
cites work: Sliding modes in intersecting switching surfaces. I: Blending
cites work: Q3994949
cites work: Uniqueness of Filippov sliding vector field on the intersection of two surfaces in \(\mathbb R^3\) and implications for stability of periodic orbits
DOI: 10.1016/J.CAM.2015.02.026
description: scientific article; zbMATH DE number 6479591