Sufficient quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints

被引：0
作者：
Osmolovskii N.P. [1 ,2 ,3 ]
机构：
[1] Systems Research Institute, Warsaw
[2] Politechnika Radomska, Radom
[3] Akademia Podlaska, Siedlce
来源：
Journal of Mathematical Sciences | 2011年 / 173卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Optimal Control Problem; Basic Constant; Critical Cone; Weak Minimum; Quadratic Condition;
D O I：
10.1007/s10958-011-0233-x
中图分类号：
学科分类号：
摘要：
We derive second-order sufficient optimality conditions for discontinuous controls in optimal control problems of ordinary differential equations with initial-final state constraints and mixed state-control constraints of equality and inequality type. Under the assumption that the gradients with respect to the control of active mixed constraints are linearly independent, the sufficient conditions imply a bounded strong minimum in the problem. © 2011 Springer Science+Business Media, Inc.
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页码：1 / 106
页数：105
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共 77 条
  • [1] Afanasiev A.P., Dikusar V.V., Milyutin A.A., Chukanov S.V., Necessary Condition for an Extremum, (1988)
  • [2] Ben-Tal A., Zowe J., Second-order optimality conditions for the L<sub>1</sub>-minimization problem, Appl. Math. Optim., 13, pp. 45-48, (1985)
  • [3] Bonnans J.F., Hermant A., Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints, Ann. I. H. P. Nonlin. Anal
  • [4] Bonnans J.F., Osmolovskii N.P., Second-order analysis of optimal control problems with control and initial-final state constraints, J. Convex Anal
  • [5] Dikusar V.V., Milyutin A.A., Qualitative and Numerical Methods for the Maximum Principle, (1989)
  • [6] Dmitruk A.V., Euler-Jacobi equation in the calculus of variations, Mat. Zametki, 20, 6, pp. 847-858, (1976)
  • [7] Dmitruk A.V., Jacobi-type conditions for positive semidefiniteness of a quadratic form on a polygonal cone with finite number of faces, Izv. Akad. Nauk SSSR, 45, 3, pp. 608-619, (1981)
  • [8] Dmitruk A.V., Jacobi-type conditions for the Bolza problem with inequalities, Mat. Zametki, 35, 6, pp. 813-827, (1984)
  • [9] Dmitruk A.V., Quadratic conditions for a Pontryagin minimum in an optimal control problem linear in control. I. Deciphering theorem, Izv. Akad. Nauk SSSR, 50, 2, pp. 284-312, (1986)
  • [10] Dmitruk A.V., Quadratic conditions for a Pontryagin minimum in an optimal control problem linear in control. II. Theorem on weakening inequality constraints, Izv. Akad. Nauk SSSR, 51, 4, pp. 812-832, (1987)
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