Symplectic Runge-Kutta discretization of a regularized forward-backward sweep iteration for optimal control problems

2019/12/15 by Xin Liu, Liu, Xin, Jason Frank +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #37M15 #49M205 #65L06 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1912.07028

openalex publication_date 2019/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Li, Chen, Tai & E. (J. Machine Learning Research, 2018) have proposed a regularization of the forward-backward sweep iteration for solving the Pontryagin maximum principle in optimal control problems. The authors prove the global convergence of the iteration in the continuous time case. In this article we show that their proof can be extended to the case of numerical discretization by symplectic Runge-Kutta pairs. We demonstrate the convergence with a simple numerical experiment.

Citations

• Anderson Acceleration for Fixed-Point Iterations

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