A computational method based on the modification of the variational iteration method for determining the solution of the optimal control problems

Abstract

AbstractThis 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.