使用克罗托夫函数进行快速合成轨迹研究
1. 基础理论与关键公式
在相关研究中，存在如下重要公式：
[
\begin{align}
&\lim_{l \to \infty} \left[ S_1(1x^l(t_1^l), t_1^l) + \psi_1(1x^l(t_0^l), t_0^l) - \psi_1(1x^l(t_1^l), t_1^l) + S_{12}(12x^l(t_{12}^l), t_{12}^l) + \psi_{11.12}(11.12x^l(t_1^l), t_1^l) - \psi_{11.12}(11.12x^l(t_{12}^l), t_{12}^l) + S_{11}(11x^l(t_{11}^l), t_{11}^l) + \psi_{11}(11x^l(t_{12}^l), t_{12}^l) - \psi_{11}(11x^l(t_{11}^l), t_{11}^l) \right] \
=& \inf_{Q_0}[\psi_1(1x(t_0), t_0)] + \inf_{Q_1}[S_1(1x(t_1), t_1) - \psi_1(1x(t_1), t_1) + \psi_{11.12}(11.12x(t_1), t_1)] + \inf_{Q_{12}}[S_{12}(12x(t_{12}), t_{12}) - \psi_{11.12}(11.12x(t_{12}), t_{12}) + \psi_{11}(11x(t_{12}), t_{12})] + \inf_{Q_{11}}[S_{11}(11x(t_{11}), t_{11}) - \psi_{11}(11x(t_{11}), t_{11})]
