Normality and second-order optimality conditions in state-constrained optimal control problems with bounded minimizers

被引：0

作者：

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

机构：

[1] Univ Porto, Fac Engn, SYSTEC ARISE, Rua Dr Roberto Frias,s-n, P-4200465 Porto, Portugal

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 366卷

关键词：

Optimal control; State constraints; Normal maximum principle; Second-order optimality conditions;

D O I：

10.1016/j.jde.2023.04.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A smooth optimal control problem with endpoint, mixed and state constraints is considered. The controllability matrix is constructed and the normality condition is presented as the condition of full rank for this matrix. The approach based on the controllability matrix allows one to examine the case of state-constrained control problems with fixed endpoints. As an application of normality, the second-order necessary optimality conditions are derived. The connection between different forms of second-order conditions is indicated. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：378 / 407

页数：30

共 50 条

[1] Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems
K. Malanowski
H. Maurer
S. Pickenhain
Journal of Optimization Theory and Applications, 2004, 123 : 595 - 617
[2] Second-order sufficient conditions for state-constrained optimal control problems
Malanowski, K
Maurer, H
Pickenhain, S
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2004, 123 (03) : 595 - 617
[3] Second-order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations
Casas, E
Tröltzsch, F
APPLIED MATHEMATICS AND OPTIMIZATION, 1999, 39 (02): : 211 - 227
[4] Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations
E. Casas
F. Tröltzsch
Applied Mathematics and Optimization, 1999, 39 : 211 - 227
[5] Second-Order Necessary Optimality Conditions in State Constrained Optimal Control
Hoehener, Daniel
2013 IEEE 52ND ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2013, : 544 - 549
[6] First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations
J. Frédéric Bonnans
Constanza de la Vega
Xavier Dupuis
Journal of Optimization Theory and Applications, 2013, 159 : 1 - 40
[7] First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations
Bonnans, J. Frederic
de la Vega, Constanza
Dupuis, Xavier
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 159 (01) : 1 - 40
[8] Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations
Casas, E
Tröltzsch, F
Unger, A
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (05) : 1369 - 1391
[9] SECOND-ORDER AND STABILITY ANALYSIS FOR STATE-CONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH SPARSE CONTROLS
Casas, Eduardo
Troeltzsch, Fredi
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (02) : 1010 - 1033
[10] Sufficient second order optimality conditions for a state-constrained optimal control problem of a weakly singular integral equation
Rösch, A
Tröltzsch, F
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2002, 23 (1-2) : 173 - 193

← 1 2 3 4 5 →