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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Vydáno v:IEEE transactions on automatic control Ročník 68; číslo 10; s. 1 - 8
Hlavní autoři: Hassan, Syeda Sakira, Sarkka, Simo
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.10.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3234236