Minimax Solutions of Hamilton--Jacobi Equations with Fractional Coinvariant Derivatives
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866914767184068608 |
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| author | Gomoyunov, Mikhail |
| author_facet | Gomoyunov, Mikhail |
| contents | We consider a Cauchy problem for a Hamilton--Jacobi equation with coinvariant derivatives of an order $α\in (0, 1)$. Such problems arise naturally in optimal control problems for dynamical systems which evolution is described by ordinary differential equations with the Caputo fractional derivatives of the order $α$. We propose a notion of a generalized in the minimax sense solution of the considered problem. We prove that a minimax solution exists, is unique, and is consistent with a classical solution of this problem. In particular, we give a special attention to the proof of a comparison principle, which requires construction of a suitable Lyapunov--Krasovskii functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_11306 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Minimax Solutions of Hamilton--Jacobi Equations with Fractional Coinvariant Derivatives Gomoyunov, Mikhail Optimization and Control Analysis of PDEs 35F21, 35D99, 26A33 We consider a Cauchy problem for a Hamilton--Jacobi equation with coinvariant derivatives of an order $α\in (0, 1)$. Such problems arise naturally in optimal control problems for dynamical systems which evolution is described by ordinary differential equations with the Caputo fractional derivatives of the order $α$. We propose a notion of a generalized in the minimax sense solution of the considered problem. We prove that a minimax solution exists, is unique, and is consistent with a classical solution of this problem. In particular, we give a special attention to the proof of a comparison principle, which requires construction of a suitable Lyapunov--Krasovskii functional. |
| title | Minimax Solutions of Hamilton--Jacobi Equations with Fractional Coinvariant Derivatives |
| topic | Optimization and Control Analysis of PDEs 35F21, 35D99, 26A33 |
| url | https://arxiv.org/abs/2011.11306 |