Optimal control based on the variational iteration method

In this study, an approach for designing an optimal control law, based on the variational iteration method, is proposed. The idea consists of formulating the problem of optimal control under a variational problem form by substituting the control variable by its expression derived from the system model in the performance index. Then, the solution of the variational problem obtained is achieved by satisfying the Euler–Lagrange equation, which is in general nonlinear. Therefore, the variational iteration method is adopted to solve the Euler–Lagrange equation obtained, and the optimal control law is easily deduced by performing simple calculations. To illustrate the suggested design approach, a nonlinear system is considered, and the result obtained is compared with the analytical solution to show the effectiveness of the proposed design approach.