APPROXIMATION OF RELAXED NONLINEAR PARABOLIC OPTIMAL-CONTROL PROBLEMS

Citation
I. Chryssoverghi et A. Bacopoulos, APPROXIMATION OF RELAXED NONLINEAR PARABOLIC OPTIMAL-CONTROL PROBLEMS, Journal of optimization theory and applications, 77(1), 1993, pp. 31-50
Citations number
22
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
ISSN journal
00223239
Volume
77
Issue
1
Year of publication
1993
Pages
31 - 50
Database
ISI
SICI code
0022-3239(1993)77:1<31:AORNPO>2.0.ZU;2-S
Abstract
We consider a relaxed optimal control problem for systems defined by n onlinear parabolic partial differential equations with distributed con trol. The problem is completely discretized by using a finite-element approximation scheme with piecewise linear states and piecewise consta nt controls. Existence of optimal controls and necessary conditions fo r optimality are derived for both the continuous and the discrete prob lem. We then prove that accumulation points of sequences of discrete o ptimal [resp. extremal] controls are optimal [resp. extremal] for the continuous problem.