Discretization methods for optimal control problems with state constraints

Chryssoverghi, I; Coletsos, I; Kokkinis, B

dc.contributor.author	Chryssoverghi, I	en
dc.contributor.author	Coletsos, I	en
dc.contributor.author	Kokkinis, B	en
dc.date.accessioned	2014-03-01T01:24:00Z
dc.date.available	2014-03-01T01:24:00Z
dc.date.issued	2006	en
dc.identifier.issn	0377-0427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17163
dc.subject	Discretization	en
dc.subject	Midpoint scheme	en
dc.subject	Optimal control	en
dc.subject	Penalized gradient projection method	en
dc.subject	Piecewise linear controls	en
dc.subject	Relaxed controls	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Approximation theory	en
dc.subject.other	Constraint theory	en
dc.subject.other	Discrete time control systems	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Optimal control systems	en
dc.subject.other	Optimization	en
dc.subject.other	Midpoint scheme	en
dc.subject.other	Optimal control	en
dc.subject.other	Piecewise linear controls	en
dc.subject.other	Relaxed controls	en
dc.subject.other	Problem solving	en
dc.title	Discretization methods for optimal control problems with state constraints	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cam.2005.04.020	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cam.2005.04.020	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We consider an optimal control problem described by nonlinear ordinary differential equations, with control and state constraints, including pointwise 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, while the controls are approximated by (not necessarily continuous) piecewise linear classical controls. 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 combined discretization-optimization method to the continuous classical problem, thus reducing computing time and memory. We prove that accumulation points of sequences generated by these methods are admissible and extremal in some sense for the corresponding discrete or continuous, classical or relaxed, problem. For nonconvex problems whose solutions are nonclassical, we show that we can apply the above methods to the problem formulated in Gamkrelidze relaxed form. Finally, numerical examples are given. (c) 2005 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/j.cam.2005.04.020	en
dc.identifier.isi	ISI:000236439800001	en
dc.identifier.volume	191	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	31	en