Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems

Chryssoverghi, I

dc.contributor.author	Chryssoverghi, I	en
dc.date.accessioned	2014-03-01T01:21:51Z
dc.date.available	2014-03-01T01:21:51Z
dc.date.issued	2005	en
dc.identifier.issn	0324-8569	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16399
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-26044475922&partnerID=40&md5=22a310b81ddfe7bacd1fd65ad9455505	en
dc.relation.uri	http://matwbn.icm.edu.pl/ksiazki/cc/cc34/cc3424.pdf	en
dc.subject	Discretization	en
dc.subject	Gradient projection method	en
dc.subject	Non-matching Runge-Kutta schemes	en
dc.subject	Optimal control	en
dc.subject	Piecewise polynomial controls	en
dc.subject.classification	Automation & Control Systems	en
dc.subject.classification	Computer Science, Cybernetics	en
dc.subject.other	NONLINEAR OPTIMAL-CONTROL	en
dc.subject.other	INTERPOLANTS	en
dc.subject.other	CONVERGENCE	en
dc.title	Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	This paper addresses the numerical solution of optimal control problems for systems described by ordinary differential equations with control constraints. The state equation is discretized by a general explicit Run-e-Kutta scheme and the controls are approximated by functions that are piecewise polynomial, but not necessarily continuous. We then propose an approximate gradient projection method that constructs sequences of discrete controls and progressively refines the discretization. Instead of using the exact discrete cost derivative, which usually requires tedious calculations, we use here an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation by the same Runge-Kutta scheme backward and the integral involved by a Newton-Cotes integration rule, both involving maximal order intermediate approximations. The main result, is that strong accumulation points in L-2, if they exist, of sequences generated by this method satisfy the weak necessary conditions for optimality for the continuous problem. In the unconstrained case and under additional assumptions, we prove strong convergence in L-2 and derive an a posteriori error estimate. Finally, numerical examples are given.	en
heal.publisher	POLISH ACAD SCIENCES SYSTEMS RESEARCH INST	en
heal.journalName	Control and Cybernetics	en
dc.identifier.isi	ISI:000233503600003	en
dc.identifier.volume	34	en
dc.identifier.issue	2	en
dc.identifier.spage	425	en
dc.identifier.epage	451	en