Higher-Order Noether's Theorem for Isoperimetric Variational Problems

被引：4

作者：

Frederico, Gasto ^{[1
,2
]}

Lazo, Matheus Jatkoske ^{[3
]}

Barreto, Maria Nilde ^{[1
]}

da Costa Sousa, Jose Vanterler ^{[4
]}

机构：

[1] Univ Fed Ceara, Campus Russas, Russas, Brazil

[2] Univ Cape Verde, Dept Sci & Technol, Praia, Santiago, Cape Verde

[3] Fed Univ Rio Grande, Inst Math Stat & Phys, Rio Grande, RS, Brazil

[4] Fed Univ ABC, Ctr Math Comp & Cognit, Santo Andre, SP, Brazil

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2023年 / 199卷 / 02期

关键词：

Higher-order Noether's theorem; Variational isoperimetric problems; DuBois-Reymond conditions; Euler-Lagrange equations; SYMMETRY THEOREM; CALCULUS;

D O I：

10.1007/s10957-023-02288-z

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this present paper, we concern a non-smooth higher-order extension of Noether's symmetry theorem for variational isoperimetric problems with delayed arguments. The result is proven to be valid in the class of Lipschitz functions, as long as the delayed higher-order Euler-Lagrange extremals are restricted to those that satisfy the delayed higher-order DuBois-Reymond necessary optimality condition. The important case of delayed isoperimetric optimal control problems is considered as well.

引用

页码：541 / 568

页数：28

共 26 条

[1] Noether's theorem on time scales [J].

Bartosiewicz, Zbigniew ;

Torres, Delfim F. M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (02) :1220-1226

[2]

Basin M, 2008, LECT NOTES CONTR INF, V380, P1

[3]

Bokov G.V., 2011, J. Math. Sci, V172, P623, DOI [10.1007/s10958-011-0208-y, DOI 10.1007/S10958-011-0208-Y]

[4]

Chiasson J., 2007, Applications of Time Delay Systems, V352

[5] Constants of motion for isoperimetric variational problems with time delay [J].

Frederico, G. S. F. ;

Lazo, M. J. ;

Barreto, M. N. F. ;

Paiva, J. .

APPLICABLE ANALYSIS, 2022, 101 (07) :2707-2725

[6]

Frederico G. S. F., 2009, Generalizations of Noether's theorem in the calculus of variations and optimal control

[7] A formulation of Noether's theorem for fractional problems of the calculus of variations [J].

Frederico, Gastao S. F. ;

Torres, Delfim F. M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 334 (02) :834-846

[8] NOETHER'S SYMMETRY THEOREM FOR VARIATIONAL AND OPTIMAL CONTROL PROBLEMS WITH TIME DELAY [J].

Frederico, Gastao S. F. ;

Torres, Delfim F. M. .

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2012, 2 (03) :619-630

[9]

Fridman E., 2014, Introduction to time-delay systems: analysis and control, DOI DOI 10.1007/978-3-319-09393-2

[10]

Gelfand I.M., 1963, Calculus of Variations

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