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Second order analysis for bang-bang control problems of PDEs

Abstract: In this paper, we derive some su?cient second order optimality conditions for control problems of partial di?erential equations (PDEs) when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it. Though not always, in this situation the optimal control is typically bang-bang. Two di?erent control problems are studied. The second di?ers from the ?rst in the presence of the L1 norm of the control. This term leads to optimal controls that are sparse and usually take only three di?erent values (we call them bang-bang-bang controls). Though the proofs are detailed in the case of a semilinear elliptic state equation, the approach can be extended to parabolic control problems. Some hints are provided in the last section to extend the results.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Casas E.,

 Fuente: SIAM Journal on Control and Optimization, 2012, 50(4), 2355-2372

Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2012

Nº de páginas: 18

Tipo de publicación: Artículo de Revista

 DOI: 10.1137/120862892

ISSN: 0363-0129,1095-7138

 Proyecto español: MTM2011-22711