A hybrid control framework for an optimal visiting problem
Fabio BagagioloDipartimento di Matematica, Università di Trento, Via Sommarive, 14, 38123 Povo (TN) ItalyAdriano FestaDipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino ItalyLuciano MarzuferoDipartimento di Matematica, Universit‘a di Trento, Via Sommarive, 14, 38123 Povo (TN) Italy
ABI
Аннотация
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.
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