The interpolated variational iteration method for solving a class of nonlinear optimal control problems

Abstract

Despite the variety of methods available to solve nonlinear optimal con-trol problems, numerical methods are still evolving to solve these problems. This paper deals with the numerical solution of nonlinear optimal control affine problems by the interpolated variational iteration method, which was introduced in 2016 to improve the variational iteration method. For this purpose, the optimality conditions are first derived as a two-point bound-ary value problem and then converted to an initial value problem with the unknown initial values for costates. The speed and convergence of the method are compared with the existing methods in the form of three ex-amples, and the initial values of the costates are obtained by an efficient technique in each iteration.

Keywords

• optimal control problems
• interpolated variational iteration method
• pontryagin’s maximum principle