Email this article Optimal control problem for the impulsive differential equations with non-local boundary conditions
- Authors: Sharifov Y.A1
-
Affiliations:
- Baku State University
- Issue: Vol 17, No 4 (2013)
- Pages: 34-45
- Section: Articles
- URL: https://ogarev-online.ru/1991-8615/article/view/20802
- DOI: https://doi.org/10.14498/vsgtu1134
- ID: 20802
Cite item
Full Text
Abstract
The optimal control problem is investigated, where the state of the controlled system is described by the impulsive differential equations with non-local boundary conditions. The existence and uniqueness of the non-local impulsive boundary problem by fixed admissible controls are proved using the contraction mapping principle. The gradient of the functional is calculated under certain conditions on the initial data. The necessary conditions for optimality of the first order are obtained.
Full Text
##article.viewOnOriginalSite##About the authors
Yagub A Sharifov
Baku State University
Email: sharifov22@rambler.ru
(Ph.D. Phys. & Math.), Associate profesor, Dept. of Mathematical Methods of Applied Analysis 23, Z. Khalilov st., Baku, AZ-1073/1, Azerbaijan
References
- А. М. Самойленко, Н. А. Перестюк, Дифференциальные уравнения с импульсным воздействием. Киев: Вища школа, 1987. 287 с.
- A. M. Samoilenko, N. A. Perestyuk, Impulsive Diff erential Equations. Singapore: World Scienti c, 1995. ix+467 pp.
- A. Halanay, D. Wexler, Teoria calitativ a a sistemelor cu impulsuri (Qualitative Theory of Sampled-Data Systems). Bucuresti: Editura Academiei Republicii Socialiste România, 1968. 312 pp.
- А. Халанай, Д. Векслер, Качественная теория импульсных систем. Москва: Мир, 1971. 309 с.
- V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of impulsive di fferential equations / Series in Modern Applied Mathematics. Vol. 6.World Scienti c: Singapore, 1989. xii+273 pp.
- M. Benchohra, J. Henderson, S. Ntouyas, Impulsive diff erential equations and inclusions / Contemporary Mathematics and Its Applications. Vol. 2. Hindawi Publishing Corporation: New York, 2006. xiv+366 pp.
- B. Selvaraj, M. Mallika Arjunan, V. Kavitha, "Existence of solutions for impulsive nonlinear diff erential equations with nonlocal conditions" // J. KSIAM, 2009. Vol. 13, no. 3. Pp. 203-215, http://mathnet.kaist.ac.kr/mathnet/thesis_file/jksiam-v13n3p203.pdf.
- A. Anguraj, M. Mallika Arjunan, "Existence and uniqueness of mild and classical solutions of impulsive evolution equations" // Electron. J. Di fferential Equations, 2005. Vol. 2005, no. 111. Pp. 1-8, http://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJDE/Volumes/2005/111/anguraj.pdf.
- S. Ji, S. Wen, "Nonlocal Cauchy problem for impulsive di fferential equations in Banach spaces" // Int. J. Nonlinear Sci, 2010. Vol. 10, no. 1. Pp. 88-95.
- M. Li, M. Han, "Existence for neutral impulsive functional di fferential equations with nonlocal conditions" // Indag. Math. (N.S.), 2009. Vol. 20, no. 3. Pp. 435-451.
- А. М. Самойленко, Н. И. Ронто, Численно-аналитические методы исследования решений краевых задач. Киев: Наукова думка, 1986. 223 с.
- Ф. П. Васильев, Методы оптимизации. Москва: Факториал Пресс, 2002. 823 с.
Supplementary files
