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Optimal control for $n× n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables

In: Mathematica Slovaca, vol. 53, no. 3
H. A. El-Saify - G. M. Bahaa
Detaily:
Rok, strany: 2003, 461 - 476
O článku:
The main goal of this paper is to study a distributed control problem for $n× n$ coupled systems of Petrowsky type with an infinite number of variables by using the theorems of J. L. Lions et al. ([LIONS, J. L.: Optimal Control of Systems Governed by Partial Differential Equations. Grundlehren Math. Wiss. 170, Springer-Verlag, Berlin-Heidelberg-New York, 1971], [LIONS, J. L.—MAGENES, E.: Non-Homogeneous Boundary Value Problem and Applications, Vol. I. Grundlehren Math. Wiss. 181, Springer-Verlag, Berlin-Heidelberg-New York, 1972]) Yet the problem considered there is more general than the one in [EL-SAIFY, H. A.: Boundary control problem with an infinite number of variables, Internat. J. Math. Math. Sci. 28 (2001), 57–62], [KOTARSKI, W.— \linebreak EL-SAIFY, H. A.—BAHAA, G. M.: Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay, IMA J. Math. Control Inform. 19 (2002), 461–476]. The controls are allowed to be in the space $(L2(0,T;L2(\Bbb R∞)))n$. The necessary and sufficient conditions for optimality of the control are obtained and the set of inequalities defining the optimal control of these systems are also obtained. This study is carried out in two directions, the first one for the problem with mixed Dirichlet conditions, and the second one for the same problem with mixed Neumann conditions. Several mathematical examples and a real example for derived optimality conditions are presented.
Ako citovať:
ISO 690:
El-Saify, H., Bahaa, G. 2003. Optimal control for $n× n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables. In Mathematica Slovaca, vol. 53, no.3, pp. 461-476. 0139-9918.

APA:
El-Saify, H., Bahaa, G. (2003). Optimal control for $n× n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables. Mathematica Slovaca, 53(3), 461-476. 0139-9918.