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A computational method based on the modification of the variational iteration method for determining the solution of the optimal control problems
Author(s) -
Kafash Behzad,
Rafiei Zahra,
Karbassi Seyed M.,
Wazwaz Abdul M.
Publication year - 2020
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2739
Subject(s) - lagrange multiplier , mathematics , optimal control , convergence (economics) , multiplier (economics) , sequence (biology) , nonlinear system , mathematical optimization , genetics , physics , quantum mechanics , biology , economics , macroeconomics , economic growth
This article presents a modification of the variational iteration method (VIM) for solving Hamilton‐Jacobi‐Bellman equations of linear and nonlinear optimal control problems. In this method, the Lagrange multiplier is chosen in such a way that a sequence of value functions that are produced by this presented method (PM) converges to exact solution faster than the standard VIM. This fast convergence is due to choosing an exponentially decaying Lagrange multiplier for the first time. Finally, some examples are presented to demonstrate the effectiveness of the PM for finding the solution of the optimal control problems.