# An improvement to the homotopy perturbation method for solving the Hamilton-Jacobi-Bellman equation

@article{Effati2013AnIT, title={An improvement to the homotopy perturbation method for solving the Hamilton-Jacobi-Bellman equation}, author={Sohrab Effati and Hassan Saberi Nik and Mohammad Shirazian}, journal={IMA J. Math. Control. Inf.}, year={2013}, volume={30}, pages={487-506} }

In this paper, the piecewise homotopy perturbation method (PHPM) is employed to solve the Hamilton– Jacobi–Bellman (HJB) equation arising in the optimal control problems. The method is a simple modification of the standard homotopy perturbation method (HPM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding HJB equation. Applying the PHPM with He’s polynomials reveals that the modified…

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