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

Xin Liu; Jason Frank

doi:10.1016/j.cam.2020.113133

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

Xin Liu^*, Jason Frank

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Li et al. (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.

Original language	English
Article number	113133
Number of pages	16
Journal	Journal of Computational and Applied Mathematics
Volume	383
DOIs	https://doi.org/10.1016/j.cam.2020.113133
Publication status	Published - Feb 2021

Bibliographical note

Funding Information:
The first author gratefully acknowledges support from the Chinese Scholarship Council under Grant No. 201607040074.

Publisher Copyright:
© 2020 The Author(s)

Funding

The first author gratefully acknowledges support from the Chinese Scholarship Council under Grant No. 201607040074.

Keywords

Nonlinear iterations
Nonlinear optimal control
Pontryagin maximum principle
Symplectic integrators

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10.1016/j.cam.2020.113133Licence: CC BY

1-s2.0-S0377042720304246-mainFinal published version, 639 KBLicence: CC BY

Cite this

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title = "Symplectic Runge–Kutta discretization of a regularized forward–backward sweep iteration for optimal control problems",

abstract = "Li et al. (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.",

keywords = "Nonlinear iterations, Nonlinear optimal control, Pontryagin maximum principle, Symplectic integrators",

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N2 - Li et al. (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.

AB - Li et al. (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.

KW - Nonlinear iterations

KW - Nonlinear optimal control

KW - Pontryagin maximum principle

KW - Symplectic integrators

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

Abstract

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Keywords

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