Modified homotopy perturbation method for optimal control problems using the Padé approximant

In this study, we propose a hybrid method that combines the homotopy perturbation method (HPM) and Padé technique to obtain the approximate analytic solution of the Hamilton–Jacobi–Bellman equation. The truncated series solution for the HPM is suitable but only in a small domain when the exact solution is not obtained. To improve the accuracy and enlarge the convergence domain, the Padé technique is applied to the series solution for the HPM. Three examples are given to illustrate the applicability, simplicity, and efficiency of the proposed method. The results obtained are then compared with the exact solution and basic HPM. We demonstrate that this hybrid method provides an approximate analytic solution with higher accuracy than the classic HPM.