DYNAMIC OPTIMAL CONTROL PROBLEMS IN HAMILTONIAN AND LAGRANGIAN SYSTEMS
This paper presents a geometric approach to the optimal control problem by developing a new formulation based on advanced ingredients of differential and Poisson geometry. Therefore, the exact optimal solution of the control problem can be obtained using an analytical methodology that converts the Hamilton-Jacobi-Bellman Partial Differential Equation (PDE) to a reduced Hamiltonian system with fewer variables. Considering the wide use of Lagrangians in solving the optimal control models, we also theorize how the reduced Lagrangian system can be achieved using the mutual relationship between the Lagrangian and Hamiltonian forms.
optimal control problem, Poisson geometry, Hamiltonian system, Lagrangian system, variational symmetry group, Hamilton-Jacobi-Bellman PDE.
Received: March 14, 2021; Accepted: April 7, 2021; Published: April 27, 2021
How to cite this article: Atefeh Hasan-Zadeh, Dynamic optimal control problems in Hamiltonian and Lagrangian systems, Advances in Differential Equations and Control Processes 24(2) (2021), 175-185. DOI: 10.17654/DE024020175
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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