Optimization and relaxation of nonlinear elliptic control systems

Kourogenis, NC; Papageorgiou, NS

dc.contributor.author	Kourogenis, NC	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:15:46Z
dc.date.available	2014-03-01T01:15:46Z
dc.date.issued	2000	en
dc.identifier.issn	0916-7005	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13722
dc.subject	elliptic inclusion	en
dc.subject	upper semicontinuous and lower semicontinuous multifunction	en
dc.subject	measurable multifunction	en
dc.subject	measurable selection	en
dc.subject	property Q	en
dc.subject	Young measure	en
dc.subject	relaxed problem	en
dc.subject	relaxability	en
dc.subject	admissible relaxation	en
dc.subject	weak convergence of measures	en
dc.subject.classification	Mathematics, Applied	en
dc.title	Optimization and relaxation of nonlinear elliptic control systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF03167377	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF03167377	en
heal.language	English	en
heal.publicationDate	2000	en
heal.abstract	In this paper we study the existence and relaxation theory for distributed parameter systems driven by nonlinear elliptic differential equations. The existence theory is developed for systems with a priori feedback (closed loop systems), while the main results of the relaxation results are proved for open loop systems. We start with some existence theorems for nonlinear elliptic inclusions which are then used to establish the existence of admissible states for the optimal control problem. Then with the help of a convexity-type condition, we formulate and prove the main existence theorem for the problem. The proof employs the so-called reduction technique. Then we formulate three different versions of the relaxed problem, we show that they are equivalent and finally we show that they have the same value as the original problem and their set of states captures the asymptotic behavior of the sequences of original states.	en
heal.publisher	KINOKUNIYA CO LTD	en
heal.journalName	JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS	en
dc.identifier.doi	10.1007/BF03167377	en
dc.identifier.isi	ISI:000165224400008	en
dc.identifier.volume	17	en
dc.identifier.issue	3	en
dc.identifier.spage	453	en
dc.identifier.epage	479	en