@article{ecbe97332d484fadb8ddb52c22ef8a43,
title = "Approximation of sweeping processes and controllability for a set-valued evolution",
abstract = "We consider a controlled evolution problem for a set \Omega (t) \subset \BbbR d, originally motivated by a model where a dog controls a flock of sheep. Necessary conditions and sufficient conditions are given, in order that the evolution be completely controllable. Similar techniques are then applied to the approximation of a sweeping process. Under suitable assumptions, we prove that there exists a control function such that the corresponding evolution of the set \Omega (t) is arbitrarily close to the one determined by the sweeping process.",
author = "Alberto Bressan and Marco Mazzola and Nguyen, {Khai T.}",
note = "Funding Information: \ast Received by the editors May 24, 2018; accepted for publication (in revised form) April 25, 2019; published electronically July 23, 2019. https://doi.org/10.1137/18M1189610 Funding: The research by the third author was partially supported by a grant from the Simons Foundation/SFARI (521811, NTK). \dagger Department of Mathematics, Penn State University, University Park, PA 16802 (axb62@ psu.edu). \ddagger Institut de Math\e'matiques de Jussieu --Paris Rive Gauche, CNRS, Sorbonne Universit\e', 4 place Jussieu, 75252 Paris, France (marco.mazzola@imj-prg.fr). \S Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (khai@ math.ncsu.edu). Funding Information: The research by the third author was partially supported by a grant from the Simons Foundation/SFARI (521811, NTK). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics.",
year = "2019",
doi = "10.1137/18M1189610",
language = "English (US)",
volume = "57",
pages = "2487--2514",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}