A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle

被引：35

作者：

Arutyunov, Aram ^{[1
]}

Karamzin, Dmitry ^{[2
]}

机构：

[1] RAS, VA Trapeznikov Inst Control Sci, Moscow, Russia

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

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2020年 / 184卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Optimal control; Maximum principle; State constraints; Regularity conditions; LIPSCHITZ CONTINUITY; LAGRANGE MULTIPLIER; SWEEPING PROCESSES; EULER-LAGRANGE; NORMALITY; APPROXIMATIONS; TRAJECTORIES;

D O I：

10.1007/s10957-019-01623-7

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：

A survey on the theory of maximum principle for state-constrained optimal control problems is presented. The focus is on such issues as regularity and controllability conditions, non-degeneracy and normality of the maximum principle, and on the continuity of the measure multiplier.

引用

页码：697 / 723

页数：27

共 79 条

[31] SQP-methods for solving optimal control problems with control and state constraints:: adjoint variables, sensitivity analysis and real-time control [J].

Büskens, C ;

Maurer, H .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 120 (1-2) :85-108

[32] Optimal control of a nonconvex perturbed sweeping process [J].

Cao, Tan H. ;

Mordukhovich, B. S. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (2-3) :1003-1050

[33] OPTIMALITY CONDITIONS FOR A CONTROLLED SWEEPING PROCESS WITH APPLICATIONS TO THE CROWD MOTION MODEL [J].

Cao, Tan H. ;

Mordukhovich, Boris S. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (02) :267-306

[34]

Chertovskih R., 2020, EUROPEAN J CONTROL

[35]

Chertovskih R., 2018, P IEEE OES AUT UND V

[36]

Clarke F.H., 1983, OPTIMIZATION NONSMOO

[37] OPTIMAL MULTIPROCESSES [J].

CLARKE, FH ;

VINTER, RB .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (05) :1072-1091

[38] Optimal control of the sweeping process over polyhedral controlled sets [J].

Colombo, G. ;

Henrion, R. ;

Hoang, Nguyen D. ;

Mordukhovich, B. S. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (04) :3397-3447

[39] Discrete Approximations of a Controlled Sweeping Process [J].

Colombo, G. ;

Henrion, R. ;

Hoang, N. D. ;

Mordukhovich, B. S. .

SET-VALUED AND VARIATIONAL ANALYSIS, 2015, 23 (01) :69-86

[40]

Colombo G., 2012, Dyn. Contin. Discrete Impuls. Syst. Ser. B, V19, P117

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