Policy iteration for the deterministic control problems -- a viscosity approach
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910907670462464 |
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| author | Tang, Wenpin Tran, Hung Vinh Zhang, Yuming Paul |
| author_facet | Tang, Wenpin Tran, Hung Vinh Zhang, Yuming Paul |
| contents | This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by adding a viscosity term via finite differences in space. We prove that PI for the semi-discrete scheme converges exponentially fast, and provide a bound on the error induced by the semi-discrete scheme. We also consider the discrete space-time scheme, where both space and time are discretized. Convergence rate of PI and the discretization error are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00419 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Policy iteration for the deterministic control problems -- a viscosity approach Tang, Wenpin Tran, Hung Vinh Zhang, Yuming Paul Optimization and Control Numerical Analysis Analysis of PDEs This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by adding a viscosity term via finite differences in space. We prove that PI for the semi-discrete scheme converges exponentially fast, and provide a bound on the error induced by the semi-discrete scheme. We also consider the discrete space-time scheme, where both space and time are discretized. Convergence rate of PI and the discretization error are studied. |
| title | Policy iteration for the deterministic control problems -- a viscosity approach |
| topic | Optimization and Control Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2301.00419 |