The Group-Theoretical Analysis of Nonlinear Optimal Control Problems with Hamiltonian Formalism
- https://doi.org/10.1080/14029251.2020.1683985How to use a DOI?
- Nonlinear optimal control problems, theory of Lie groups, dynamic optimization, Hamiltonian formalism, Pontryagin’s maximum principle, economic growth models
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.
- © 2020 The Authors. Published by Atlantis and Taylor & Francis
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- 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 -