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POLAT, GÜLDEN GÜN

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Dr. Öğr. Üyesi

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POLAT

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GÜLDEN GÜN

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2020 - 20213
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Now showing 1 - 3 of 3
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    PublicationOpen Access
    The group-theoretical analysis of nonlinear optimal control problems with hamiltonian formalism
    (2020-01-02) Özer, Teoman; POLAT, GÜLDEN GÜN; 166389; 153145
    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.
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    On Group Analysis of Optimal Control Problems in Economic Growth Models
    (American Institute of Mathematical Sciences, 2020) POLAT, GÜLDEN GÜN; Özer, Teoman
    The optimal control problems in economic growth theory are analyzed by considering the Pontryagin's maximum principle for both current and present value Hamiltonian functions based on the theory of Lie groups. As a result of these necessary conditions, two coupled first-order differential equations are obtained for two different economic growth models. The first integrals and the analytical solutions (closed-form solutions) of two different economic growth models are analyzed via the group theory including Lie point symmetries, Jacobi last multiplier, Prelle-Singer method,_-symmetry and the mathematical relations among them.
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    PublicationOpen Access
    On Ramsey Dynamical Model and Closed-Form Solutions
    (Springer Nature, 2021) POLAT, GÜLDEN GÜN; Özer, Teoman
    This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions of maximum principle are analyzed and then first integrals and corresponding closed-form (analytical) solutions are determined by using Lie point symmetries in conjunction with Prelle-Singer and Jacobi last multiplier methods. Additionally, associated lambda-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.