An approximate-analytical solution for the Hamilton–Jacobi–Bellman equation via homotopy perturbation method

In this paper, we give an analytical-approximate solution for the Hamilton–Jacobi–Bellman (HJB) equation arising in optimal control problems using He’s polynomials based on homotopy perturbation method (HPM). Applying the HPM with He’s polynomials, solution procedure becomes easier, simpler and more straightforward. The comparison of the HPM results with the exact solution, Modal series and measure theoretical method are made. Some illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.