ON HIGHER-ORDER STATE CONSTRAINTS

被引：4

作者：

Karamzin, Dmitry ^{[1
]}

Pereira, Fernando Lobo ^{[1
]}

机构：

[1] Univ Porto, SYSTEC ARISE, Fac Engn, Rua Dr Roberto Frias S-N 4200-465, Porto, Portugal

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2023年 / 61卷 / 04期

关键词：

optimal control; higher-order state constraints; maximum principle; MAXIMUM PRINCIPLE; STABILITY;

D O I：

10.1137/22M1487497

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A higher-order state-constrained optimal control problem is considered. A nondegenerate maximum principle is obtained based on the corresponding inward and outward pointing conditions of the higher order. Simple examples demonstrate how the new optimality conditions exclude degenerate sets of Lagrange multipliers, while the conventional approach fails to do so. The conservation law is derived as a consequence of extremality. The connection to the classical form of optimality conditions is investigated.

引用

页码：1913 / 1933

页数：21

共 25 条

[1]

Arutyunov A., 1993, Mat. Sb., V184, P3

[2] Properties of extremals in optimal control problems with state constraints [J].

Arutyunov, A. V. ;

Karamzin, D. Yu. .

DIFFERENTIAL EQUATIONS, 2016, 52 (11) :1411-1422

[3] 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

[4] 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

[5]

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

[6] 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

[7] Investigation of Controllability and Regularity Conditions for State Constrained Problems [J].

Arutyunov, Aram V. ;

Karamzin, Dmitry Yu. ;

Pereira, Fernando L. .

IFAC PAPERSONLINE, 2017, 50 (01) :6295-6302

[8] Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice [J].

Betts, J. T. ;

Campbell, S. L. ;

Engelsone, A. .

OPTIMIZATION AND ENGINEERING, 2007, 8 (01) :1-19

[9] Regular path-constrained time-optimal control problems in three-dimensional flow fields [J].

Chertovskih, R. ;

Karamzin, D. ;

Khalil, N. T. ;

Lobo Pereira, F. .

EUROPEAN JOURNAL OF CONTROL, 2020, 56 :98-106

[10] An Indirect Method for Regular State-Constrained Optimal Control Problems in Flow Fields [J].

Chertovskih, Roman ;

Karamzin, Dmitry ;

Khalil, Nathalie T. ;

Pereira, Fernando Lobo .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2021, 66 (02) :787-793

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