TY - JOUR

T1 - The Group-Theoretical Analysis of Nonlinear Optimal Control Problems with Hamiltonian Formalism

AU - Polat, Gülden Gün

AU - Özer, Teoman

N1 - Publisher Copyright:
© 2019, © 2019 the authors.

PY - 2020/1/2

Y1 - 2020/1/2

N2 - 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.

AB - 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.

KW - dynamic optimization

KW - economic growth models

KW - Hamiltonian formalism

KW - Nonlinear optimal control problems

KW - Pontryagin’s maximum principle

KW - theory of Lie groups

UR - http://www.scopus.com/inward/record.url?scp=85074490282&partnerID=8YFLogxK

U2 - 10.1080/14029251.2020.1683985

DO - 10.1080/14029251.2020.1683985

M3 - Article

AN - SCOPUS:85074490282

SN - 1402-9251

VL - 27

SP - 106

EP - 129

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 1

ER -