APPLICATION OF THE AVERAGING METHOD TO THE PROBLEMS OF OPTIMAL CONTROL OF THE IMPULSE SYSTEMS

被引：6

作者：

Koval'chuk, T. V. ^{[1
]}

Mogylova, V. V. ^{[2
]}

Stanzhytskyi, O. M. ^{[3
]}

Shovkoplyas, T. V. ^{[3
]}

机构：

[1] Kyiv Natl Univ Trade & Econ, 19 Kioto Str, UA-02156 Kiev, Ukraine

[2] Natl Tech Univ Ukraine, Igor Sikorsky Kyiv Polytech Inst, 7 Peremogy Av, UA-03056 Kiev, Ukraine

[3] Taras Shevchenko Natl Univ Kyiv, 64-13 Volodymyrska Str, UA-01601 Kiev, Ukraine

来源：

CARPATHIAN MATHEMATICAL PUBLICATIONS | 2020年 / 12卷 / 02期

关键词：

optimal control problem; optimal control; exact problem; averaged problem; valid control; averaging condition; weak convergence; compactness; semi-continuity; quality criterion; minimizing sequence;

D O I：

10.15330/cmp.12.2.504-521

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The problem of optimal control at finite time interval for a system of differential equations with impulse action at fixed moments of time as well as the corresponding averaged system of ordinary differential equations are considered. It is proved the existence of optimal control of exact and averaged problems. Also, it is established that optimal control of averaged problem realize the approximate optimal synthesis of exact problem. The main result of the article is a theorem, where it is proved that optimal contol of an averaged problem is almost optimal for exact problem. Substantiation of proximity of solutions of exact and averaged problems is obtained.

引用

页码：504 / 521

页数：18

共 10 条

[1]

Kovalchuk T.V., 2020, J MATH SCI, V247, P314, DOI [10.1007/s10958-020-04804-2, DOI 10.1007/S10958-020-04804-2]

[2] APPLICATION OF THE METHOD OF AVERAGING TO THE PROBLEMS OF OPTIMAL CONTROL OVER FUNCTIONAL-DIFFERENTIAL EQUATIONS [J].

Kravets', V. I. ;

Koval'chuk, T. V. ;

Mohyl'ova, V. V. ;

Stanzhyts'kyi, O. M. .

UKRAINIAN MATHEMATICAL JOURNAL, 2018, 70 (02) :232-242

[3] Averaging method in some problems of optimal control [J].

Nosenko, T. V. ;

Stanzhyts'kyi, O. M. .

NONLINEAR OSCILLATIONS, 2008, 11 (04) :539-547

[4]

Plotnikov V.A., 1992, Averaging Method in Control Problems

[5] On the averaging of differential equations on an infinite interval [J].

Samoilenko, AM ;

Stanzhitskii, AN .

DIFFERENTIAL EQUATIONS, 2006, 42 (04) :505-511

[6]

Samoilenko AM., 1995, IMPULSIVE DIFFERENTI, DOI 10.1142/2892

[7]

Samoilenko AM., 1971, MATH PHYS, V9, P101

[8]

Stanzhitskii A.M., 2001, Ukrainian Math. J., V53, P323, DOI [10.1023/A:1010437625118, DOI 10.1023/A:1010437625118]

[9] Study of optimal control problems on the half-line by the averaging method [J].

Stanzhitskii, A. N. ;

Dobrodzii, T. V. .

DIFFERENTIAL EQUATIONS, 2011, 47 (02) :264-277

[10]

Yosida K., 1965, FUNCTIONAL ANAL

← 1 →