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arXiv · 1805.09125

Approximation of Sweeping Processes and Controllability for a Set Valued Evolution

Alberto Bressan·Marco Mazzola·Khai T. Nguyen
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Abstract

We consider a controlled evolution problem for a set $\Omega(t)\in\mathbb{R}^d$, 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.

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Alberto Bressan, Marco Mazzola, Khai T. Nguyen. 2018-05-23. Approximation of Sweeping Processes and Controllability for a Set Valued Evolution. https://arxiv.org/abs/1805.09125

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