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...

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Detalhes bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Kunisch, Karl
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
Descrição
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.