Infinite horizon optimal control problems with discount factor on the state, Part I: analysis of the controlled state equation
This is the first part of an investigation of infinite horizon optimal control problems subject to semilinear parabolic equations. A discount factor on the state variable is introduced in the cost. This allows for the treatment of infinite horizon problems without stabilizability assumptions. The no...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/29305 |
| Acesso em linha: | https://hdl.handle.net/10902/29305 |
| Access Level: | acceso abierto |
| Palavra-chave: | Semilinear parabolic equations Infinite horizon Discount factor Differentiability of the control-to-state mapping |
| Resumo: | This is the first part of an investigation of infinite horizon optimal control problems subject to semilinear parabolic equations. A discount factor on the state variable is introduced in the cost. This allows for the treatment of infinite horizon problems without stabilizability assumptions. The nonlinearities can be of polynomial type, thus covering reaction-diffusion equations which are important for applications. The control-to-state mapping and its regularity are analyzed in detail. This involves the relation between the type of the nonlinearity and the discount factor. |
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