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.

中文翻译：

---

一种基于变分迭代法修正的计算方法，用于确定最优控制问题的解

本文提出了变分迭代方法（VIM）的一种修改形式，用于求解线性和非线性最优控制问题的Hamilton-Jacobi-Bellman方程。在这种方法中，拉格朗日乘数的选择方式是，通过此提出的方法（PM）生成的值函数序列收敛到比标准VIM更快的精确解。这种快速收敛是由于首次选择了指数衰减的拉格朗日乘数。最后，通过一些例子说明了PM在寻找最优控制问题的解决方案方面的有效性。