Fourier-Hermite Dynamic Programming for Optimal Control

Syeda Sakira Hassan, Simo Sarkka

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)6377-6384
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number10
Early online date4 Jan 2023
Publication statusPublished - 1 Oct 2023
MoE publication typeA1 Journal article-refereed


  • approximate dynamic programming
  • Convergence
  • Costs
  • differential dynamic programming
  • Dynamic programming
  • Fourier–Hermite series
  • Heuristic algorithms
  • Jacobian matrices
  • Optimal control
  • sigma-point dynamic programming
  • Taylor series
  • trajectory optimization


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