Fourier-Hermite Dynamic Programming for Optimal Control

• 成果类型: Article
• 署名作者: Hassan, Syeda Sakira; Sarkka, Simo
• 署名单位: Aalto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3234236
• 发表日期: 2023
• 页码: 6377-6384
• 关键词: approximate dynamic programming; differential dynamic programming; Fourier-Hermite series; sigma-point dynamic programming; Trajectory optimization

摘要

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.