A computational method based on the modification of the variational iteration method for determining the solution of the optimal control problems. (18th March 2020)

• Record Type: Journal Article
• Authors: Kafash, Behzad; Rafiei, Zahra; Karbassi, Seyed M.; Wazwaz, Abdul M.
• Other Names: De Gersem Herbert guestEditor.; Kurz Stefan guestEditor.; Schöps Sebastian guestEditor.; Geuzaine Christophe guestEditor.
• Is Part Of: International journal of numerical modelling. Volume 33:Number 5(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-03-18
• Subjects: Banach fixed point theorem -- Hamilton‐Jacobi‐Bellman equations -- modification of the variational iteration method -- optimal control problems; Electric networks -- Mathematical models -- Periodicals; Electronics -- Mathematical models -- Periodicals; 621.3011
• DOI: 10.1002/jnm.2739
• Languages: English
• ISSNs: 0894-3370

Abstract

Abstract: 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.