On Normality in Optimal Control Problems with State Constraints

被引：1

作者：

Karamzin, D. Yu. ^{[1
]}

Pereira, F. Lobo ^{[2
]}

机构：

[1] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Moscow, Russia

[2] Univ Porto, Res Ctr Syst & Technol SYSTEC, Porto, Portugal

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2023年 / 63卷 / 06期

基金：

俄罗斯科学基金会;

关键词：

optimal control; maximum principle; state constraints; normality; MAXIMUM PRINCIPLE; DEGENERACY; EQUALITY;

D O I：

10.1134/S0965542523060118

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general optimal control problem with endpoint, mixed and state constraints is considered. The question of normality of the known necessary optimality conditions is investigated. Normality stands for the positiveness of the Lagrange multiplier & lambda;(0) corresponding to the cost functional. In order to prove the normality condition, an appropriate derivative operator for the state constraints is constructed, which acts in a specific Hilbert space and has the properties of surjection and continuity.

引用

页码：973 / 989

页数：17

共 30 条

[1] Non-degenerate necessary optimality conditions for the optimal control problem with equality-type state constraints [J].

Arutyunov, A. V. ;

Karamzin, D. Yu. .

JOURNAL OF GLOBAL OPTIMIZATION, 2016, 64 (04) :623-647

[2] ON SOME CONTINUITY PROPERTIES OF THE MEASURE LAGRANGE MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR STATE CONSTRAINED PROBLEMS [J].

Arutyunov, A. V. ;

Karamzin, D. Yu. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (04) :2514-2540

[3] The Maximum Principle for Optimal Control Problems with State Constraints by RV Gamkrelidze: Revisited [J].

Arutyunov, A. V. ;

Karamzin, D. Y. ;

Pereira, F. L. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 149 (03) :474-493

[4] Maximum principle in problems with mixed constraints under weak assumptions of regularity [J].

Arutyunov, A. V. ;

Karamzin, D. Yu. ;

Pereira, F. L. .

OPTIMIZATION, 2010, 59 (07) :1067-1083

[5]

Arutyunov A.V., 2000, Optimality condition: abnormal and degenerate problems

[6]

Arutyunov A. V., 2017, P IFAC C TOUL FRANC

[7] Investigation of Conditions for Non-degeneracy and Normality in Control Problems with Equality and Inequality State Constraints [J].

Arutyunov, Aram ;

Karamzin, Dmitry ;

Pereira, Fernando L. .

IFAC PAPERSONLINE, 2020, 53 (02) :6869-6874

[8] A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle [J].

Arutyunov, Aram ;

Karamzin, Dmitry .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2020, 184 (03) :697-723

[9] STATE CONSTRAINTS IN OPTIMAL-CONTROL - THE DEGENERACY PHENOMENON [J].

ARUTYUNOV, AV ;

ASEEV, SM .

SYSTEMS & CONTROL LETTERS, 1995, 26 (04) :267-273

[10]

Bettiol P, 2016, J CONVEX ANAL, V23, P291

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