HYBRID CONTROL AND QUASI-VARIATIONAL HAMILTON-JACOBI INEQUALITIES, NUMERICAL ASPECTS AND APPLICATION TO SAILING NAVIGATION AND TRAFFIC PROBLEMS - ADRIANO FESTA - DISMA - POLITECNICO DI TORINO

Abstract In this seminar we discuss the extension of the classic dynamic programming approach to hybrid control systems, where a continuous controller can switch between a finite collection of states, paying a cost of switching.
This approach requires the resolution of a system of quasi-variational Hamilton-Jacobi inequalities that we propose to approximate via a semi-Lagrangian scheme obtained by the direct discretization of the dynamical programming principle. We discuss the application of such a framework to model a sailing boat navigation problem for the optimization of the strategic choices on a racecourse and the optimal management of the traffic on a multi-lane road, using a mean-field game inspired model.

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