Fourier--Hermite Dynamic Programming for Optimal Control

TL;DR

This paper introduces a Fourier--Hermite series-based dynamic programming method for solving non-linear optimal control problems, offering quadratic convergence and improved computational efficiency over traditional Taylor series approaches.

Contribution

It presents a novel sigma-point based dynamic programming approach using Fourier--Hermite series, with proven quadratic convergence and demonstrated superior performance.

Findings

Quadratic convergence of the proposed method.

Effective approximation of the action-value function.

Enhanced performance compared to existing methods.

Abstract

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.