A Semi-Analytic Method for Solving a Class of Non-Linear Optimal Control Problems

This paper, proposes an approximate analytical method to solvea class of optimal control problems. This method is an enhancementof the variational iteration method (VIM) which is called modified variational iteration method (MVIM) and eliminates all additional calculations in VIM, thus requires less time to do the calculations. In thisapproach, first, the optimal control problem is converted into a non-linear two-point boundary value problem via the Pontryagins maximum principle, and then we applied the MVIM method to solve this boundary value problem. This suggested method is suitable for a large class of non-linear optimal control problems that for the non-linear part of the problem, we used the Taylor series expansion. In the end, three examples are provided to demonstrate the simplicity and efficiency of the method. The numerical results of the proposed method versus other methods are presented in tables. All calculations were carried out using Mathematica software.

Keywords:

Modified variational iteration method (MVIM) , Differential equations , Optimal control problems , Numerical solution