The moments sliding vector field on the intersection of two manifolds
type: Item
instance of: scholarly article
title: The moments sliding vector field on the intersection of two manifolds
zbMATH Open document ID: 1366.34024
published in: Journal of Dynamics and Differential Equations
publication date: 2017-04-20T00:00:00Z
review text: The paper is concerned with the piecewise smooth differential system \[ \dot x=f(x),\,\,\,f(x)=f_i(x),\,\,x\in R_i,\,\,i=1,\ldots,N,\,\,t\in [0,T], \] where \(R_i\subseteq \mathbb{R}^n\) are open, disjoint and connected sets with \(\mathbb{R}^n=\overline{\cup R_i}\), on each region \(R_i\) the function \(f\) is given by a smooth vector field \(f_i\), and \(\Sigma_i:=\{x\in\mathbb{R}^n,\,\,h_i(x)=0\}\), \(i=1,\ldots,p\), (\(2^p=N\)), with \(h_i\) smooth scalar valued functions (at least \(C^2\)), with specific interest in the case \(N=4\). The authors associate a quadrilateral to the attractivity configuration of \(\Sigma=\Sigma_1\cap\Sigma_2\), and then they investigate this geometrical configuration. They prove that the moments vector field (which belongs to the class of Filipov vector fields) is well-defined and smoothly exiting at generic first order exit points, and discuss other cases enjoying this property. Numerical experiments which support the main results are also presented.
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 6706445
zbMATH Keywords: piecewise smooth systems
zbMATH Keywords: Filippov sliding motion
zbMATH Keywords: attractive co-dimension 2 manifold
zbMATH Keywords: moments solution
author: Luca Dieci
author: Fabio V. Difonzo
reviewed by: Rodica Luca
MaRDI profile type: Publication
full work available at URL: s10884-015-9439-9
OpenAlex ID: W2029323011
cites work: Numerical methods for nonsmooth dynamical systems. Applications in mechanics and electronics
cites work: Sliding modes in intersecting switching surfaces. I: Blending
cites work: Piecewise-smooth dynamical systems. Theory and applications
cites work: Sliding motion on the intersection of two manifolds: spirally attractive case
cites work: A comparison of Filippov sliding vector fields in codimension 2
cites work: On the inverse of some sign matrices and on the moments sliding vector field on the intersection of several manifolds: nodally attractive case
cites work: A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis
cites work: Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field
cites work: Q3994508
cites work: Mean value coordinates
cites work: Solving Ordinary Differential Equations I
cites work: A global analysis of matrices of functions of several variables
cites work: Dynamics at a Switching Intersection: Hierarchy, Isonomy, and Multiple Sliding
cites work: Regularization of discontinuous vector fields on \({\mathbb{R}^3}\) via singular perturbation
cites work: Q3995527
cites work: An event-driven method to simulate Filippov systems with accurate computing of sliding motions
cites work: Sliding modes in control and optimization. Transl. from the Russian
DOI: 10.1007/S10884-015-9439-9
description: scientific article; zbMATH DE number 6706445