IJPAM: Volume 1, No. 3 (2002)

OPTIMAL CONTROL PROBLEM FOR A
HYPERBOLIC SYSTEM WITH MIXED
CONTROL-STATE CONSTRAINTS
INVOLVING OPERATOR OF
INFINITE ORDER

W. Kotarski$^1$, H.A. El-Saify$^2$, G.M. Bahaa$^3$
$^1$Institute of Informatics
Silesian University
Bedzinska 60, 41-200 Sosnowiec, POLAND
e-mail: kotarski@gate.math.us.edu.pl
$^{2,3}$Dept. of Mathematics
Faculty of Science
Cairo University, Beni Suef, EGYPT
$^2$e-mail: elsaify$_{-}$ah@hotmail.com
$^3$e-mail: bahaas99@yahoo.com


Abstract.A distributed control problem for a hyperbolic system with mixed constraints on states and controls involving operator of infinite order is considered. The performance index is more general than the quadratic one and has an integral form. Making use of the Dubovitskii-Milyutin theorem, necessary and sufficient conditions of optimality are derived for the Dirichlet problem. Yet the problem considered there is more general than the one in [7]-[10], [23], [24].

Received: January 28, 2002

AMS Subject Classification: 49J20, 93C20, 49K20, 35K20

Key Words and Phrases: infinite order hyperbolic operators, distributed control problems, Dirichlet problem, Dubovitskii-Milyutin theorem, conical approximations, necessary and sufficient conditions of optimality

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 3