In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, given an optimal control, we build up an upper bound for the number of its switching points; show that it jumps from one direction to the reverse direction at each switching point; give its dynamic behaviour between two consecutive switching points; and study its switching directions.

中文翻译：

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关于线性ODE的时间最优控制的切换特性

在本文中，我们介绍了具有球形控制约束的线性ODE的时间最优控制的一些属性。更准确地说，给定最佳控制，我们为其开关点的数量建立了上限；表明它在每个切换点从一个方向跳到另一个方向；在两个连续的切换点之间给出其动态行为；并研究其切换方向。