Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems

被引：18

作者：

Krasovskii, A. A. ^{[1
]}

Tarasyev, A. M. ^{[1
]}

机构：

[1] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620219, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2008年 / 262卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Hamiltonian System; Optimal Control Problem; STEKLOV Institute; Optimal Trajectory; Pontryagin Maximum Principle;

D O I：

10.1134/S0081543808030103

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an optimal control problem with a functional defined by an improper integral. We study the concavity properties of the maximized Hamiltonian and analyze the Hamiltonian systems in the Pontryagin maximum principle. On the basis of this analysis, we propose an algorithm for constructing an optimal trajectory by gluing the dynamics of the Hamiltonian systems. The algorithm is illustrated by calculating an optimal economic growth trajectory for macroeconomic data.

引用

页码：121 / 138

页数：18

共 50 条

[21] A Proof of the Pontryagin Maximum Principle for Initial-Value Problems
Hartberger, R. J.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1973, 11 (02) : 139 - 145
[22] The Pontryagin Maximum Principle and Sufficient Optimality Conditions for Nonlinear Problems
A. V. Arutyunov
[J]. Differential Equations, 2003, 39 : 1671 - 1679
[23] The hybrid maximum principle is a consequence of pontryagin maximum principle
Dmitruk, A. V.
Kaganovich, A. M.
[J]. SYSTEMS & CONTROL LETTERS, 2008, 57 (11) : 964 - 970
[24] Regularized Lagrange principle and Pontryagin maximum principle in optimal control and in inverse problems
Sumin, M., I
[J]. TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2019, 25 (01): : 279 - 296
[25] Application of Pontryagin's principle of maximum to the inverse problems of scattering
Batrakov, DO
Tarasov, MM
[J]. MMET 2000: INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ELECTROMAGNETIC THEORY, VOLS 1 AND 2, CONFERENCE PROCEEDINGS, 2000, : 621 - 623
[26] THE PONTRYAGIN MAXIMUM PRINCIPLE FOR MINIMAX PROBLEMS OF OPTIMAL-CONTROL
BARRON, EN
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (12) : 1155 - 1165
[27] Regularized Lagrange Principle and Pontryagin Maximum Principle in Optimal Control and Inverse Problems
Sumin, Mikhail I.
[J]. IFAC PAPERSONLINE, 2018, 51 (32): : 871 - 876
[28] Pontryagin’s maximum principle for optimal impulsive control problems
A. V. Arutyunov
D. Yu. Karamzin
F. Pereira
[J]. Doklady Mathematics, 2010, 81 : 418 - 421
[29] Pontryagin's maximum principle for constrained impulsive control problems
Arutyunov, A. V.
Karamzin, D. Yu.
Pereira, F.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (03) : 1045 - 1057
[30] Pontryagin's Maximum Principle for Optimal Impulsive Control Problems
Arutyunov, A. V.
Karamzin, D. Yu.
Pereira, F.
[J]. DOKLADY MATHEMATICS, 2010, 81 (03) : 418 - 421

← 1 2 3 4 5 →