Approximation of Sweeping Processes and Controllability for a Set Valued Evolution
Résumé
We consider a controlled evolution problem for a set Ω(t) ∈ IR 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 Ω(t) is arbitrarily close to the one determined by the sweeping process.
Domaines
Mathématiques [math]
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Bressan et al. - 2019 - Approximation of Sweeping Processes and Controllab.pdf (327.1 Ko)
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