A single player and a mass of agents: a pursuit evasion-like game
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912248593645568 |
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| author | Bagagiolo, Fabio Capuani, Rossana Marzufero, Luciano |
| author_facet | Bagagiolo, Fabio Capuani, Rossana Marzufero, Luciano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05742 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A single player and a mass of agents: a pursuit evasion-like game Bagagiolo, Fabio Capuani, Rossana Marzufero, Luciano Optimization and Control Analysis of PDEs 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. |
| title | A single player and a mass of agents: a pursuit evasion-like game |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2302.05742 |