On viscosity solutions of path-dependent Hamilton--Jacobi--Bellman--Isaacs equations for fractional-order systems
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866914767210283008 |
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| author | Gomoyunov, Mikhail I. |
| author_facet | Gomoyunov, Mikhail I. |
| contents | This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $α\in (0, 1)$ and a Bolza cost functional. The differential game is associated to the Cauchy problem for the path-dependent Hamilton--Jacobi--Bellman--Isaacs equation with so-called fractional coinvariant derivatives of the order $α$ and the corresponding right-end boundary condition. A notion of a viscosity solution of the Cauchy problem is introduced, and the value functional of the differential game is characterized as a unique viscosity solution of this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_02451 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On viscosity solutions of path-dependent Hamilton--Jacobi--Bellman--Isaacs equations for fractional-order systems Gomoyunov, Mikhail I. Optimization and Control Analysis of PDEs 26A33, 34A08, 49L25, 35D40 This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $α\in (0, 1)$ and a Bolza cost functional. The differential game is associated to the Cauchy problem for the path-dependent Hamilton--Jacobi--Bellman--Isaacs equation with so-called fractional coinvariant derivatives of the order $α$ and the corresponding right-end boundary condition. A notion of a viscosity solution of the Cauchy problem is introduced, and the value functional of the differential game is characterized as a unique viscosity solution of this problem. |
| title | On viscosity solutions of path-dependent Hamilton--Jacobi--Bellman--Isaacs equations for fractional-order systems |
| topic | Optimization and Control Analysis of PDEs 26A33, 34A08, 49L25, 35D40 |
| url | https://arxiv.org/abs/2109.02451 |