The problem of controlling the vibrations of a string with given inseparable values of the deflection function and velocities at intermediate times is considered. By the method of separation of variables, the problem reduces to the problem of controlling ordinary differential equations with given initial, final, and unseparated multipoint intermediate conditions. The problem is solved using methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions. As an application of the proposed approach, a control action is constructed for the control problem of string vibrations with specified unseparated conditions on the values of the deflection function and string velocities at two intermediate points in time.

中文翻译：

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在中间时间点具有不可分多点条件的弦振动控制问题

考虑了在给定的挠曲函数和速度在中间时刻具有不可分离的值的情况下控制弦的振动的问题。通过变量分离的方法，问题减少到控制具有给定的初始，最终和未分离的多点中间条件的常微分方程的问题。使用具有多点中间条件的有限维系统控制理论的方法解决了该问题。作为所提出的方法的一种应用，针对在两个中间时间点的偏转函数和琴弦速度的值具有指定的不可分离条件的琴弦振动的控制问题，构造了控制动作。