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

Gülden Gün Polat, Teoman Özer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)106-129
Number of pages24
JournalJournal of Nonlinear Mathematical Physics
Volume27
Issue number1
DOIs
Publication statusPublished - 2 Jan 2020

Bibliographical note

Publisher Copyright:
© 2019, © 2019 the authors.

Keywords

  • dynamic optimization
  • economic growth models
  • Hamiltonian formalism
  • Nonlinear optimal control problems
  • Pontryagin’s maximum principle
  • theory of Lie groups

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