In this paper, we study the well−posedness (in the sense of existence and uniqueness of a solution) of a discontinuous sweeping process involving prox-regular sets in Hilbert spaces. The variation of the moving set is controlled by a positive Radon measure and the perturbation is assumed to satisfy a Lipschitz property. The existence of a solution with bounded variation is achieved thanks to the Moreau’s catching-up algorithm adapted to this kind of problem. Various properties and estimates of jumps of the solution are also provided. We give sufficient conditions to ensure the uniform prox-regularity when the moving set is described by inequality constraints. As an application, we consider a nonlinear differential complementarity system which is a combination of an ordinary differential equation with a nonlinear complementarily condition. Such problems appear in many areas such as nonsmooth mechanics, nonregular electrical circuits and control systems.
Accepté le :
DOI : 10.1051/cocv/2016053
Mots-clés : Variational analysis, measure differential inclusions, sweeping process, prox-regular set, B.V. solutions, Moreau’s catching-up algorithm, nonlinear differential complementarity systems
@article{COCV_2017__23_4_1293_0,
author = {Adly, Samir and Nacry, Florent and Thibault, Lionel},
title = {Discontinuous sweeping process with prox-regular sets},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1293--1329},
publisher = {EDP-Sciences},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016053},
mrnumber = {3716922},
zbl = {1379.49023},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2016053/}
}
TY - JOUR AU - Adly, Samir AU - Nacry, Florent AU - Thibault, Lionel TI - Discontinuous sweeping process with prox-regular sets JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1293 EP - 1329 VL - 23 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016053/ DO - 10.1051/cocv/2016053 LA - en ID - COCV_2017__23_4_1293_0 ER -
%0 Journal Article %A Adly, Samir %A Nacry, Florent %A Thibault, Lionel %T Discontinuous sweeping process with prox-regular sets %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1293-1329 %V 23 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016053/ %R 10.1051/cocv/2016053 %G en %F COCV_2017__23_4_1293_0
Adly, Samir; Nacry, Florent; Thibault, Lionel. Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1293-1329. doi : 10.1051/cocv/2016053. http://www.numdam.org/articles/10.1051/cocv/2016053/
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