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The relaxed stochastic maximum principle in singular optimal control of diffusions
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.ORCID-id: 0000-0002-6608-0715
2007 (Engelska)Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 46, nr 2, s. 427-444Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

This paper studies optimal control of systems driven by stochastic differential equations, where the control variable has two components, the first being absolutely continuous and the second singular. Our main result is a stochastic maximum principle for relaxed controls, where the first part of the control is a measure valued process. To achieve this result, we establish first order optimality necessary conditions for strict controls by using strong perturbation on the absolutely continuous component of the control and a convex perturbation on the singular one. The proof of the main result is based on the strict maximum principle, Ekeland's variational principle, and some stability properties of the trajectories and adjoint processes with respect to the control variable.

Ort, förlag, år, upplaga, sidor
2007. Vol. 46, nr 2, s. 427-444
Nyckelord [en]
singular control, maximum principle, adjoint process, variational, inequality, relaxed control, variational principle
Identifikatorer
URN: urn:nbn:se:kth:diva-16674DOI: 10.1137/050644744ISI: 000246923600003Scopus ID: 2-s2.0-41449088749OAI: oai:DiVA.org:kth-16674DiVA, id: diva2:334717
Anmärkning
QC 20100525Tillgänglig från: 2010-08-05 Skapad: 2010-08-05 Senast uppdaterad: 2017-12-12Bibliografiskt granskad

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Djehiche, Boualem

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