Discretization-optimization methods for optimal control problems

Chryssoverghi, I

dc.contributor.author	Chryssoverghi, I	en
dc.date.accessioned	2014-03-01T01:22:12Z
dc.date.available	2014-03-01T01:22:12Z
dc.date.issued	2005	en
dc.identifier.issn	11092769	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16486
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-29844454535&partnerID=40&md5=9b38405b8be88b76f07f0344d75c207d	en
dc.relation.uri	http://www.wseas.us/e-library/conferences/2005corfu/c1/papers/498-222.pdf	en
dc.subject	Discretization	en
dc.subject	Midpoint scheme	en
dc.subject	Optimal control	en
dc.subject	Penalized gradient projection method	en
dc.subject	Piecewise constant controls	en
dc.subject	Relaxed controls	en
dc.subject.other	Approximation theory	en
dc.subject.other	Control system analysis	en
dc.subject.other	Gradient methods	en
dc.subject.other	Nonlinear control systems	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Optimization	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Piecewise linear techniques	en
dc.subject.other	Discrete classical problem	en
dc.subject.other	Discretization	en
dc.subject.other	Midpoint scheme	en
dc.subject.other	Penalized gradient projection method	en
dc.subject.other	Piecewise constant controls	en
dc.subject.other	Relaxed controls	en
dc.subject.other	Optimal control systems	en
dc.title	Discretization-optimization methods for optimal control problems	en
heal.type	journalArticle	en
heal.publicationDate	2005	en
heal.abstract	We consider an optimal control problem described by nonlinear ordinary differential equations, with control and state constraints. Since this problem may have no classical solutions, it is also formulated in relaxed form. The classical control problem is then discretized by using the implicit midpoint scheme for state approximation, while the controls are approximated by piecewise constant classical ones. We first study the behavior in the limit of properties of discrete optimality, and of discrete admissibility and extremality. We then apply a penalized gradient projection method to each discrete classical problem, and also a corresponding progressively refining discretization-optimization method to the continuous classical problem, thus reducing computing rime and memory. We show that accumulation points of sequences generated by these methods are admissible and extremal for the corresponding discrete or continuous, classical or relaxed, problem. For nonconvex problems whose solutions are non-classical, we show that we can apply the above methods to the problem formulated in the Gamkrelidze form. Finally, numerical examples are given.	en
heal.journalName	WSEAS Transactions on Mathematics	en
dc.identifier.volume	4	en
dc.identifier.issue	3	en
dc.identifier.spage	125	en
dc.identifier.epage	132	en