Fourier–Hermite Dynamic Programming for Optimal Control

In this article, we propose a novel computational method for solving nonlinear optimal control problems. The method is based on the use of Fourier–Hermite series for approximating the action-value function arising in dynamic programming instead of the conventional Taylor-series expansion used in differential dynamic programming. The coefficients of the Fourier–Hermite series can be numerically computed by using sigma-point methods, which leads to a novel class of sigma-point-based dynamic programming methods. We also prove the quadratic convergence of the method and experimentally test its performance against other methods.