Fourier-Hermite Dynamic Programming for Optimal Control

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 diff...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 10; pp. 1 - 8
Main Authors: Hassan, Syeda Sakira, Sarkka, Simo
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
approximate dynamic programming
Convergence
Costs
differential dynamic programming
Dynamic programming
Fourier series
Fourier–Hermite series
Heuristic algorithms
Jacobian matrices
Nonlinear control
Optimal control
Series expansion
sigma-point dynamic programming
Taylor series
trajectory optimization
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3234236