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.

中文翻译：

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正则向前-向后扫描迭代的辛Runge-Kutta离散化，用于最优控制问题

Li等。（2018）提出了正反扫描迭代的正则化方法，以解决最优控制问题中的庞特里亚金最大原理。作者证明了在连续时间情况下迭代的全局收敛性。在本文中，我们证明了它们的证明可以推广到辛格朗格-库塔对的数值离散化情况。我们用一个简单的数值实验证明了收敛性。