We present a new numerical indirect method to solve optimal control problems with degenerate equilibrium points. When the optimal control problem is autonomous, the corresponding canonical system becomes an autonomous system of ordinary differential equations. Combining the well-known blow-up technique of vector fields with the classic backward integration method, and focusing on a specific type of degenerate singular points, we develop a new method that is both easy to implement and able to deal with complex problems.

中文翻译：

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退化平衡点最优控制问题的改进后向积分方法

我们提出了一种新的数值间接方法来解决退化平衡点的最优控制问题。当最优控制问题是自治的时，相应的正则系统成为常微分方程的自治系统。将著名的向量场爆炸技术与经典的后向积分方法相结合，并针对特定类型的退化奇异点，我们开发了一种易于实现且能够处理复杂问题的新方法。