Hiperbolik Bir Sistemde Başlangıç Konumunun Optimal Kontrolü Üzerine

Bu makalede Dirichlet koşuluna sahip hiperbolik system ile yönetilen optimal kontrol problem göz önüne alınır. Optimal çözümün var ve tek olduğu kanıtlanır ve eşlenik problem elde edilir. Eşlenik problemden yararlanılarak amaç fonksiyonunun gradyeni hesaplanır. Hiperbolik sistem için gerekli optimallik şartları türetilir.

Anahtar Kelimeler:

Optimal Kontrol, Hiperbolik Denklemler, Frechet Türev

On Optimal Control of the Initial Status in a Hyperbolic System

In this study, optimal control problem governed by a hyperbolic problem with Dirichlet conditions is considered. It is demonstrated that the optimal solution for the considered optimal control problem is exist and unique and it is obtained adjoint problem. Derivative of the cost functional is calculated utilizing from adjoint problem. Finally, necessary optimality conditions for hyperbolic system are derived.

Keywords:

Optimal Control, Hyperbolic Equations, Frechet Derivative,

PDF

___

Tagiyev R. K., 2012. On Optimal Control of the Hyperbolic Equation Coefficients, Automation and Remote Control, 1145-1155.
Kröner A., 2011. Adaptive Finite Element Methods for Optimal Control of Second Order Hyperbolic Equations, Computational Methods in Applied Mathematics, 214-240.
Bahaa G. M.,Tharwat M.M., 2011. Optimal control problem for infinite variables hyperbolic systems with time lags, Archieves of Control Sciences, 21, 4, 373-393.
Bahaa G. M., 2012. Boundary Control Problem of Infinite Order Distributed Hyperbolic Systems Involving Time Lags, Intelligent Control and Automation, 3, 211-221.
Subaşı M., Güngör H., Araz İ.S., 2017. On the Control of End Point Tensions in a Vibration Problem, International Journal of Modeling and Optimization, 7, 2, 74-77.
Yeloğlu T., Subaşı M., 2010. Simultaneous control of the source terms in a vibrational string problem, Iranian Journal of Science & Technology, Transaction A, Vol. 34, No. A1.
Ju Eun-Young, Jeong Jin-Mun, 2013. Optimal control problems for hyperbolic equations with damping terms involving p-Laplacian, Journal of Inequalities and Applications, 92.
Hwang J., Nakagiri S, 2010. Optimal control problems for the equation of motion of membrane with strong viscosity. J. Math. Anal. Appl. 321, 327-342, 19.
Lions, J.L., 1971. Optimal Control of Systems Governed by Partial Differential Equations. Springer, Berlin.
Ladyzhenskaya O. A., 1985. Boundary Value Problems in Mathematical Physics, Springer-Verlag, 322 p, New York.
Goebel, M., 1979. On Existence of Optimal Control. Math. Nachr., Vol 93, 67-73.
Yosida, K., 1980. Functional Analysis, Springer-Verlag, 624 p, New York.
Vasilyev, F.P., 1981. Ekstremal problemlerin çözüm metotları. Nauka, 400.