On the response of autonomous sweeping processes to periodic perturbations
type: Item
instance of: scholarly article
title: On the response of autonomous sweeping processes to periodic perturbations
zbMATH Open document ID: 1362.34031
author: Mikhail Kamenskii
author: Oleg Makarenkov
published in: Set-Valued and Variational Analysis
publication date: 2017-01-26T00:00:00Z
full work available at URL: http://hdl.handle.net/20.500.11824/335
review text: The authors consider an autonomous sweeping process of the form \[ - \dot{u}(t) \in N_B(u(t)) + f_0(u(t)),\,\,u \in \mathbb{R}^2,\tag{1} \] where \(B = \{x \in \mathbb{R}^2: \|x\| \leq 1 \}\) and \(N_B(x) = \{\xi \in \mathbb{R}^2: \langle \xi, c -x \rangle \leq 0 \,\,\forall c \in C \}\) is the outward normal cone to \(B.\) It is supposed that system (1) possesses a boundary equilibrium \(u_\star \in \partial B,\) i.e., \(f_0(u_\star) \in - N_B(u_\star)\) and \(f_0(u_\star) \neq 0\). Sufficient conditions under which the equilibrium \(u_\star\) persists under periodic perturbations \(f_\varepsilon (t,u)\) of \(f_0\) are studied.
reviewed by: Valerii V. Obukhovskij
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 6678149
zbMATH Keywords: sweeping process
zbMATH Keywords: differential inclusion
zbMATH Keywords: periodic solution
zbMATH Keywords: periodic perturbation
zbMATH Keywords: equilibrium
MaRDI profile type: Publication
OpenAlex ID: W1827159146
cites work: Q3324260
cites work: Mixed semicontinuous perturbation of nonconvex state-dependent sweeping process
cites work: The dynamics of discrete mechanical systems with perfect unilateral constraints
cites work: Q3234709
cites work: Q5694960
cites work: Nonsmooth mechanics. Models, dynamics and control.
cites work: Asymptotic Stability of Periodic Solutions for Nonsmooth Differential Equations with Application to the Nonsmooth van der Pol Oscillator
cites work: Bifurcations from nondegenerate families of periodic solutions in Lipschitz systems
cites work: Continuation Theorems for Periodic Perturbations of Autonomous Systems
cites work: BV periodic solutions of an evolution problem associated with continuous moving convex sets
cites work: Periodic solutions of some nonlinear differential equations
cites work: Condensing multivalued maps and semilinear differential inclusions in Banach spaces
cites work: A continuation principle for a class of periodically perturbed autonomoussystems
cites work: Polyhedral sweeping processes with oblique reflection in the space of regulated functions
cites work: Lipschitz continuous data dependence of sweeping processes in BV spaces
cites work: Q2765778
cites work: Stability and convergence of mechanical systems with unilateral constraints
cites work: Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction
cites work: Evolution problem associated with a moving convex set in Hilbert space
cites work: Q4105330
cites work: A proximal-like method for a class of second order measure-differential inclusions describing vibro-impact problems
cites work: CONTINUOUS DEPENDENCE ON DATA FOR VIBRO-IMPACT PROBLEMS
cites work: A continuity method for sweeping processes
cites work: Q3150781
cites work: Convergence of a time-stepping scheme for rigid-body dynamics and resolution of Painlevé's problem
cites work: Reformulations of measure differential inclusions and their closed graph property
cites work: Sweeping process with regular and nonregular sets.
cites work: Sweeping process with unbounded nonconvex perturbation
cites work: Lipschitz approximation of the sweeping (or Moreau) process
DOI: 10.1007/S11228-015-0348-1
Recommended article: Q5103806
Recommended article: On perturbed sweeping process
Recommended article: On periodic evolution equations governed by sweeping processes with multivalued perturbations
Recommended article: Global stability of almost periodic solutions to monotone sweeping processes and their response to non-monotone perturbations
Recommended article: Q3074324
Recommended article: On almost periodic trajectories of control systems with feedback in the form of sweeping processes
Recommended article: Q4962934
Recommended article: Lyapunov pairs for perturbed sweeping processes
Recommended article: Q4061289
Recommended article: Autonomous stochastic perturbations of dynamical systems
description: scientific article; zbMATH DE number 6678149