Inserted: 22 dec 2020
Last Updated: 12 jan 2022
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 discuss a hybrid control-based approach where the discontinuous part of the trajectory switches between a group of discrete states related to the targets of the problem. After introducing the problem, we show the well-position establishing a correspondence with a collection of time-dependent optimal stopping problems.
Keywords: optimal control of hybrid systems, generalized solutions of Hamilton-Jacobi equations, output feedback control