Fourier-Hermite Dynamic Programming for Optimal Control - Hassan, Syeda Sakira; Sarkka, Simo (IEEE transactions on automatic control, 2023)
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.