Optimal bounds for POD approximations of infinite horizon control problems based on time derivatives
In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton– Jacobi–Bellman equation that is approximated by a fully discrete method. It is known that the numerical problem is difficult t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/718517 |
| Acceso en línea: | http://hdl.handle.net/10486/718517 https://dx.doi.org/10.1007/s10915-025-02833-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Dynamic Programming Hamilton–Jacobi–Bellman equation Optimal Control Proper Orthogonal Decomposition Snapshots based on time derivatives Error Analysis Matemáticas |
| Sumario: | In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton– Jacobi–Bellman equation that is approximated by a fully discrete method. It is known that the numerical problem is difficult to handle by the so called curse of dimensionality. To mitigate this issue we apply a reduction of the order by means of a new proper orthogonal decomposition (POD) method based on time derivatives. We carry out the error analysis of the method using recently proved optimal bounds for the fully discrete approximations. Moreover, the use of snapshots based on time derivatives allows us to bound some terms of the error that could not be bounded in a standard POD approach. Some numerical experiments show the good performance of the method in practice |
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