Calculus of Variations and Geometric Measure Theory

F. Bagagiolo - A. Festa - L. Marzufero

Hybrid control for optimal visiting problems for a single player and for a crowd

created by marzufero on 22 Dec 2020
modified on 12 Jan 2022


Published Paper

Inserted: 22 dec 2020
Last Updated: 12 jan 2022

Journal: Nonlinear Differential Equations and Applications
Volume: 29
Number: 1
Year: 2022
Doi: 10.1007/s00030-021-00737-0

ArXiv: 2012.08596 PDF


In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid control-based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. The model is subsequently adapted to a mean-field framework to study viability and crowd fluxes to model a multitude of indistinguishable players.

Keywords: optimal control, Hamilton-Jacobi equations, Mean-Field Games, hybrid systems