Fourier–Hermite Dynamic Programming for Optimal Control
- Resource Type
- Periodical
- Authors
- Hassan, S.S.; Sarkka, S.
- Source
- IEEE Transactions on Automatic Control IEEE Trans. Automat. Contr. Automatic Control, IEEE Transactions on. 68(10):6377-6384 Oct, 2023
- Subject
- Signal Processing and Analysis
Dynamic programming
Costs
Taylor series
Convergence
Optimal control
Heuristic algorithms
Jacobian matrices
Approximate dynamic programming
differential dynamic programming
Fourier–Hermite series
sigma-point dynamic programming
trajectory optimization
- Language
- ISSN
- 0018-9286
1558-2523
2334-3303
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.