The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close as possible to a collection of target points. The problem does not verify the dynamic programming principle, and it needs a specific formulation to keep track of the visited target points. In this paper, we introduce a hybrid approach by adding a discontinuous part of the trajectory switching between a group of discrete states related to the targets. Then, we show the well-posedness of the related Hamilton-Jacobi problem, by reformulating the optimal visiting as a collection of time-dependent optimal stopping problems.
A hybrid control framework for an optimal visiting problem / Bagagiolo, F.; Festa, A.; Marzufero, L.. - 54:(2021), pp. 241-246. (Intervento presentato al convegno 7th IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2021 tenutosi a bel nel 2021) [10.1016/j.ifacol.2021.08.505].
A hybrid control framework for an optimal visiting problem
Festa A.;
2021
Abstract
The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close as possible to a collection of target points. The problem does not verify the dynamic programming principle, and it needs a specific formulation to keep track of the visited target points. In this paper, we introduce a hybrid approach by adding a discontinuous part of the trajectory switching between a group of discrete states related to the targets. Then, we show the well-posedness of the related Hamilton-Jacobi problem, by reformulating the optimal visiting as a collection of time-dependent optimal stopping problems.File | Dimensione | Formato | |
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BagagioloFestaMarzufero2021-2.pdf
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IFACProc_definitiva.pdf
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https://hdl.handle.net/11583/2950656