Local infimum and a family of maximum principles in optimal control

被引：8

作者：

Avakov, E. R. ^{[1
,2
]}

Magaril-Il'yaev, G. G. ^{[2
,3
,4
]}

机构：

[1] Russian Acad Sci, VA Trapeznikov Inst Control Sci, Moscow, Russia

[2] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia

[3] Russian Acad Sci, Kharkevich Inst, Inst Informat Transmiss Problems, Moscow, Russia

[4] Russian Acad Sci, Southern Math Inst, Vladikavkaz Sci Ctr, Vladikavkaz, Russia

来源：

SBORNIK MATHEMATICS | 2020年 / 211卷 / 06期

关键词：

local infimum; optimal trajectory; maximum principle; sliding regime;

D O I：

10.1070/SM9234

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of a local infimum for the optimal control problem, which generalizes the notion of an optimal trajectory, is introduced. For a local infimum the existence theorem is proved and necessary conditions in the form of a family of 'maximum principles' are derived. The meaningfulness of the necessary conditions, which generalize and strengthen Pontryagin's maximum principle, is illustrated by examples. Bibliography: 9 titles.

引用

页码：750 / 785

页数：36

共 9 条

[1]

Alekseev V. M., 1979, CONT SOVIET MATH, DOI [10.1007/978-1-4615-7551-1, DOI 10.1007/978-1-4615-7551-1]

[2]

Avakov ER, 2013, USP MAT NAUK, V68, P5, DOI DOI 10.4213/rm9525

[3]

[Аваков Евгений Рачиевич Avakov Evgeniy Rachievich], 2012, [Математические заметки, Mathematical Notes, Matematicheskie zametki], V91, P813, DOI 10.4213/mzm9383

[4]

Ekeland I., 1976, STUD MATH APPL, V1

[5]

Filippov A. F., 1959, VESTN MOSKOV U MMAFK, P25

[6]

Gamkrelidze R. V., 1977, MATH CONCEPTS METHOD, V7

[7]

Ioffe A. D., 1974, STUD MATH APPL, V6

[8]

Pontryagin L. S., 1961, MATH THEORY OPTIMAL

[9]

Zorich, 1984, UNIVERSITEXT

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