Approximation of sweeping processes and controllability for a set-valued evolution

Alberto Bressan, Marco Mazzola, Khai T. Nguyen

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)2487-2514
Number of pages28
JournalSIAM Journal on Control and Optimization
Volume57
Issue number4
DOIs
StatePublished - Jan 1 2019

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Sweeping Process
Controllability
Flock
Evolution Problems
Control Function
Approximation
Necessary Conditions
Subset
Sufficient Conditions
Model

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Cite this

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Approximation of sweeping processes and controllability for a set-valued evolution. / Bressan, Alberto; Mazzola, Marco; Nguyen, Khai T.

In: SIAM Journal on Control and Optimization, Vol. 57, No. 4, 01.01.2019, p. 2487-2514.

Research output: Contribution to journalArticle

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