  In this paper, we propose a novel computational method for solving non-linear
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 (DDP). 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.
