We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport equation type. Using also an adapted concept of non-anticipating strategies, we derive an infinite dimensional Isaacs equation, and by dynamic programming techniques we prove that the value function is the unique viscosity solution on a suitable invariant subset of a Hilbert space.
Bagagiolo, F., Capuani, R., Marzufero, L. (2024). A single player and a mass of agents: a pursuit evasion-like game. ESAIM. COCV, 30 [10.1051/cocv/2024009].
A single player and a mass of agents: a pursuit evasion-like game
Capuani, Rossana;
2024-01-01
Abstract
We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport equation type. Using also an adapted concept of non-anticipating strategies, we derive an infinite dimensional Isaacs equation, and by dynamic programming techniques we prove that the value function is the unique viscosity solution on a suitable invariant subset of a Hilbert space.| File | Dimensione | Formato | |
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