# Fourier--Hermite Dynamic Programming for Optimal Control

arXiv: https://arxiv.org/abs/2202.13453 · HTML: https://mlsanity.com/paper/2202.13453/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2022.

## Built on by (most cited first, 2 of 2)

- [Deterministic Trajectory Optimization through Probabilistic Optimal Control](https://mlsanity.com/paper/2407.13316/) (2024)
- [Recursive Entropic Variational Inference for Nonlinear State-Space Models](https://mlsanity.com/paper/2511.15409/) (2025)

## Abstract (arXiv)

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.