Abstract

We consider a system with two degrees of freedom (a pendulum on a trolley) in the case where one restricted control force is applied to the trolley. The task of a time-optimal horizontal movement to the required distance from the given equilibrium position to another identical state with the suppression of oscillations is solved. Trajectories that meet the necessary optimality conditions for the asymptotically close nonlinear system (when the mass of the pendulum is negligible in comparison with the mass of the trolley) are constructed. The results are compared with the known optimal solutions for a linearized system.

中文翻译：

---

摆式小车的时间最优运动

摘要

我们将一个具有两个自由度的系统（小车上的摆锤）应用于一个有限的控制力的情况。解决了将时间最佳水平移动到从给定平衡位置到另一个相同状态的所需距离并抑制振荡的任务。构造满足渐近闭合非线性系统（当摆的质量与手推车的质量相比可忽略不计时）的必要最优条件的轨迹。将结果与线性系统的已知最佳解决方案进行比较。