Differential Games for a Mixed ODE-PDE System
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916528707862528 |
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| author | Garavello, Mauro Rossi, Elena Sylla, Abraham |
| author_facet | Garavello, Mauro Rossi, Elena Sylla, Abraham |
| contents | Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two players act through their respective controls to influence the evolution of the system with the aim of minimizing their objective functionals $\mathcal F_1$ and $\mathcal F_2$, under the assumption that $\mathcal F_1 +\mathcal F_2 = 0$. First we prove a well posedness and a stability result for the differential system, once the control functions are fixed. Then we introduce the concept of non-anticipating strategies for both players and we consider the associated value functions, which solve two infinite-dimensional Hamilton-Jacobi-Isaacs equations in the viscosity sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential Games for a Mixed ODE-PDE System Garavello, Mauro Rossi, Elena Sylla, Abraham Analysis of PDEs Optimization and Control 35Q91, 91A23, 91A80, 35L65 Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two players act through their respective controls to influence the evolution of the system with the aim of minimizing their objective functionals $\mathcal F_1$ and $\mathcal F_2$, under the assumption that $\mathcal F_1 +\mathcal F_2 = 0$. First we prove a well posedness and a stability result for the differential system, once the control functions are fixed. Then we introduce the concept of non-anticipating strategies for both players and we consider the associated value functions, which solve two infinite-dimensional Hamilton-Jacobi-Isaacs equations in the viscosity sense. |
| title | Differential Games for a Mixed ODE-PDE System |
| topic | Analysis of PDEs Optimization and Control 35Q91, 91A23, 91A80, 35L65 |
| url | https://arxiv.org/abs/2412.12712 |