In this paper, a feedback control law is proposed to solve the asymptotic tracking problem for a ball bouncing in a triangular billiard. This controller is designed by firstly transforming the billiard table into a surface on which the ball moves without experiencing any impact, i.e. by reflecting the billiard table rather than the ball trajectory and designing a position feedback controller based on such an unfolded billiard table. Furthermore, it is shown how such an infinite-billiard table can be mapped to the surface of a torus, thus leading to bounded trajectories of the ball.

中文翻译：

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通过展开和折叠台球桌对三角台球中弹跳球的轨迹跟踪

本文提出了一种反馈控制律来解决三角台球中弹跳的渐近跟踪问题。该控制器的设计首先将台球台转化为球在不受任何冲击的情况下在其上运动的表面，即反映台球台而不是球的轨迹，并基于这种展开的台球台设计位置反馈控制器。此外，还展示了如何将这种无限台球桌映射到圆环的表面，从而导致球的有界轨迹。