On Optimal Control of the Initial Status in a Hyperbolic System

Year 2018, , 94 - 98, 30.11.2018

Seda İğret Araz

https://doi.org/10.17714/gumusfenbil.439669

Abstract

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

Hiperbolik Bir Sistemde Başlangıç Konumunun Optimal Kontrolü Üzerine

Abstract

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.

Keywords

Optimal Kontrol, Hiperbolik Denklemler, Frechet Türev

References

• 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.