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 language | English (US) |
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Pages (from-to) | 2487-2514 |
Number of pages | 28 |
Journal | SIAM Journal on Control and Optimization |
Volume | 57 |
Issue number | 4 |
DOIs | |
State | Published - 2019 |
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics