We study the problem of bringing a linear chain of masses connected by springs to an equilibrium in finite time by means of a control force applied to the first mass. We describe explicitly the desired feedback control and establish its local equivalence to the minimum-time one. We prove the robustness of the control with respect to unknown disturbances and compute the time of transfer as well as its asymptotic estimate with respect to the length of the chain.

中文翻译：

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线性振荡器链的鲁棒反馈控制

我们研究了通过施加在第一个质量上的控制力使由弹簧连接的线性质量链在有限时间内达到平衡的问题。我们明确地描述了所需的反馈控制，并建立了它与最小时间控制的局部等效性。我们证明了控制相对于未知干扰的鲁棒性，并计算了传输时间及其相对于链长度的渐近估计。