TWO-POINT BOUNDARY VALUE PROBLEM OF DYNAMICAL SYSTEMS

Authors

А. Sakenkyzy
S.A. Aisagaliev Al-Farabi Kazakh National University

Keywords:

two-point boundary value problem, necessary and sufficient conditions, solution construction, minimizing sequence, optimal control.

Abstract

A new method for solving the two-point boundary value problem of linear ordinary differential equations has been developed. The necessary and sufficient conditions for the existence of a solution to a boundary value problem with boundary conditions from given convex and closed sets are obtained. A method is proposed for constructing a solution to a boundary value problem by immersing the initial problem to a special initial optimal control problem. The basis of the proposed method for solving the boundary value problem is the solvability and construction of a general solution of the Fredholm integral equation of the first kind with a fixed parameter.

References

Понтрягин Л. С. Обыкновенные дифференциальные уравнения.-М.: Наука, 1970.- 332с.

Петровский И. Г. Лекции по теории обыкновенных дифференциальных уравнений.

-М.: Наука,1965.-272с.

Смирнов В.И. Курс высшей математики. Том III.часть 2.-М.: Наука, 1974-672с.

Матвеев Н.М. Методы интегрирования обыкновенных дифференциальных уравнений.- Минск,"Высшая школа 1974-766с.

Красовский Н.Н. Теория управления движением. -М.: Наука, 1968, -475с.

Тихонов А.Н., Васильева А.Б., Свешников А.Г. Дифференциальные уравнения.-М.:Наука, 1985-232с.

Aisagaliev S.A. Constructive method for Solvability of Fredholm equation of the first kind

// Electronic Journal of Qualitative Theory of Differential Equationsehis (EJQTDE),2017, No.72, DOI: 10. 14232/ejqtde.2017.

Aisagaliev S.A. To the boundary value problem of ordinary differential equations// Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE), 2015, No.57, p.1-17 DOI: 10.14232/ejqtde.2015.

Aisagaliev S.A. On Periodic Solutions of Autonomous Systems// Journal of Mathematical Sciences (United States), Volume 229, Issue 4, March, 2018, p.335-353.

Aisagaliev S.A. Aizermans problem in absolute stability theory for regulated systems// Sbornig Mathematics (SB MATH) ,2018,209, DOI: 10.1070/SM 8948,p.780-801.

Aisagaliev S.A. Controllability of differential equation systems// Differential Equations. Vol. 27,No.9,1991.p.1037-1047.

Aisagaliev S.A., Aisagalieva S.S. A constructure method for solving the controllability problem for ordinary differential equations// Differential Equations, Vol.29,XXX4. 1993,p.471- 482.

Aisagaliev S.A.,Belogurov A.P. Controllability and Speed of the process described by a parabolic equation with bounded control//Siberian Mathematical Journal,2012. Vol.53, XXX1,p.13-28.

Aisagaliev S.A. Optimal control of linear systems with fixed trajectory end points and bounded control// Differential Equations,-1996.-vol.32,XXX5.p.1017-1023.

Aisagaliev S.A.,Kabidoldanova A.A. On the Optimal Control of linear systems with linear performance criterion and constraints//Differential Equations,2012.-vol.48,XXX6, p.826- 836.

Aisagaliev S.A. Certain problems of bynchrinization(непонятно) theory// Journal inverse

[I] Posed Problems.-XXX21,2013.-p.159-175.

Aisagaliev S.A. Aioanov Sh.A. A remark of of the global asymptotic siability theory of phase system// Differential Equations (35), 8,1999,p. 1019-1025.

Aisagaliev S.A. Absolute stability in controlled systems // Differential Equations,vol.30,XXX5, 1994.p.687-695.

Aisagaliev S.A. To the solution of a boundary value problem with a parameter for ordinary differential equations// ISSN 2074-1863. Ufa Mathematical Journal.vol.8,No.3(2016). p.3- 13.

Айсагалиев С.А. Теория краевых задач динамических систем.-Алматы: 2021.-565с.

Айсагалиев С.А. Качественная теория интегро- дифференциальных уравнений.-Алматы: 2022.-272с.