Journal of Nonlinear Mathematical Physics

Volume 27, Issue 1, October 2019, Pages 106 - 129

The Group-Theoretical Analysis of Nonlinear Optimal Control Problems with Hamiltonian Formalism

Authors
Gülden Gün Polat
Department of Mathematics and Computer Science, İstanbul Kültür University, Bakırköy, İstanbul, 34156 Turkey, g.polat@iku.edu.tr
Teoman Özer*
Department of Civil Engineering, İstanbul Technical University, 34469 Maslak, İstanbul, Turkey, tozer@itu.edu.tr
*Corresponding author
Corresponding Author
Teoman Özer
Received 27 December 2018, Accepted 12 July 2019, Available Online 25 October 2019.
DOI
https://doi.org/10.1080/14029251.2020.1683985How to use a DOI?
Keywords
Nonlinear optimal control problems, theory of Lie groups, dynamic optimization, Hamiltonian formalism, Pontryagin’s maximum principle, economic growth models
Abstract

In this study, we pay attention to novel explicit closed-form solutions of optimal control problems in economic growth models described by Hamiltonian formalism by utilizing mathematical approaches based on the theory of Lie groups. For this analysis, the Hamiltonian functions, which are used to define an optimal control problem, are considered in two different types, namely, the current and present value Hamiltonians. Furthermore, the first-order conditions (FOCs) that deal with Pontrygain maximum principle satisfying both Hamiltonian functions are considered. FOCs for optimal control in the problem are studied here to deal with the first-order coupled systems. This study mainly focuses on the analysis of these systems concerning for to the theory of symmetry groups and related analytical approaches. First, Lie point symmetries of the first-order coupled systems are derived, and then by using the relationships between symmetries and Jacobi last multiplier method, the first integrals and corresponding invariant solutions for two different economic models are investigated. Additionally, the solutions of initial-value problems based on the transversality conditions in the optimal control theory of economic growth models are analyzed.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
106 - 129
Publication Date
2019/10
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1683985How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Gülden Gün Polat
AU  - Teoman Özer
PY  - 2019
DA  - 2019/10
TI  - The Group-Theoretical Analysis of Nonlinear Optimal Control Problems with Hamiltonian Formalism
JO  - Journal of Nonlinear Mathematical Physics
SP  - 106
EP  - 129
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683985
DO  - https://doi.org/10.1080/14029251.2020.1683985
ID  - Polat2019
ER  -