On One Damping Problem for a Nonstationary Control System with Aftereffect
- Authors: Adkhamova A.S.1, Skubachevskii A.L.1
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Affiliations:
- Peoples’ Friendship University of Russia (RUDN University)
- Issue: Vol 65, No 4 (2019): Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University
- Pages: 547-556
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/23049
- DOI: https://doi.org/10.22363/2413-3639-2019-65-4-547-556
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Abstract
We consider a control system described by the system of differential-difference equations of neutral type with variable matrix coefficients and several delays. We establish the relation between the variational problem for the nonlocal functional describing the multidimensional control system with delays and the corresponding boundary-value problem for the system of differential-difference equations. We prove the existence and uniqueness of the generalized solution of this boundary-value problem.
About the authors
A. S. Adkhamova
Peoples’ Friendship University of Russia (RUDN University)
Author for correspondence.
Email: ami_adhamova@mail.ru
Moscow, Russia
A. L. Skubachevskii
Peoples’ Friendship University of Russia (RUDN University)
Email: skublector@gmail.com
Moscow, Russia
References
- Каменский Г.А., Мышкис А.Д. К постановке краевых задач для дифференциальных уравнений с отклоняющимся аргументом и несколькими старшими членами// Диф. уравн. - 1974. -10, № 3. - C. 409-418.
- Красовский Н.Н. Теория управления движением. - М.: Наука, 1968.
- Кряжимский А.В., Максимов В.И., Осипов Ю.С. О позиционном моделировании в динамических системах// Прикл. мат. мех. - 1983. -47, № 6. - C. 883-890.
- Леонов Д.Д. К задаче об успокоении системы управления с последействием// Соврем. мат. Фундам. направл. - 2010. -37. - C. 28-37.
- Осипов Ю.С. О стабилизации управляемых систем с запаздыванием// Дифф. уравн. - 1965. -1, № 5. - C. 605-618.
- Скубачевский А.Л. К задаче об успокоении системы управления с последействием// Докл. РАН. - 1994. -335, № 2. - C. 157-160.
- Adkhamova A.S., Skubachevskii A.L. Damping problem for multidimensional control system with delays// В сб.: «Distributed computer and communication networks. 19th international conference, DCCN 2016, Moscow, Russia, November 21-25, 2016. Revised selected papers». - Cham: Springer, 2016. - C. 612-623.
- Banks H.T., Kent G.A. Control of functional differential equations of retarded and neutral type to target sets in function space// SIAM J. Control Optim. - 1972. - 10, № 4. - C. 567-593.
- Halanay A. Optimal controls for systems with time lag// SIAM J. Control Optim. - 1968. -6. - C. 213- 234.
- Kent G.A. A maximum principle for optimal control problems with neutral functional differential systems// Bull. Am. Math. Soc. - 1971. -77, № 4. - C. 565-570.
- Skubachevskii A.L. Elliptic functional differential equations and applications. - Basel-Boston-Berlin: Birkhauser, 1997.
