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
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.