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Infinite horizon optimal control problems with discount factor on the state, Part I: analysis of the controlled state equation

Abstract: 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.

 Fuente: SIAM Journal on Control and Optimization, 2023, 61(3), 1375-1393

 Editorial: Society for Industrial and Applied Mathematics

 Fecha de publicación: 09/06/2023

 Nº de páginas: 19

 Tipo de publicación: Artículo de Revista

 DOI: 10.1137/22M149027

 ISSN: 0363-0129,1095-7138

 Proyecto español: PID2020-114837GB-I00