Approximate relaxed descent method for optimal control problems

Chryssoverghi, I; Coletsos, J; Kokkinis, B

dc.contributor.author	Chryssoverghi, I	en
dc.contributor.author	Coletsos, J	en
dc.contributor.author	Kokkinis, B	en
dc.date.accessioned	2014-03-01T01:16:10Z
dc.date.available	2014-03-01T01:16:10Z
dc.date.issued	2001	en
dc.identifier.issn	0324-8569	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13958
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0347608274&partnerID=40&md5=2e4e768e392e279f3436404729a28e98	en
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0347608274&partnerID=40&md5=2e4e768e392e279f3436404729a28e98	en
dc.subject	Descent method	en
dc.subject	Discretization	en
dc.subject	Optimal control	en
dc.subject	Relaxed controls	en
dc.subject.classification	Automation & Control Systems	en
dc.subject.classification	Computer Science, Cybernetics	en
dc.subject.other	DISCRETE APPROXIMATION	en
dc.title	Approximate relaxed descent method for optimal control problems	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. Since no convexity assumptions are made on the data, the problem is reformulated in relaxed form. The relaxed state equation is discretized by the implicit trapezoidal scheme and the relaxed controls are approximated by piecewise constant relaxed controls. We then propose a combined descent and discretization method that generates sequences of discrete relaxed controls and progressively refines the discretization. Since here the adjoint of the discrete state equation is not defined, we use, at each iteration, an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation and the integral involved by appropriate trapezoidal schemes. It is proved that accumulation points of sequences constructed by this method satisfy the strong relaxed necessary conditions for optimality for the continuous problem. Finally, the computed relaxed controls can be easily approximated by piecewise constant classical controls.	en
heal.publisher	POLISH ACAD SCIENCES SYSTEMS RESEARCH INST	en
heal.journalName	Control and Cybernetics	en
dc.identifier.isi	ISI:000177298300001	en
dc.identifier.volume	30	en
dc.identifier.issue	4	en
dc.identifier.spage	X	en
dc.identifier.epage	404	en