中文摘要：

基于非线性系统反馈线性化方法得到了欠驱动Euler—Lagrangian系统的局部反馈线性化模型，并进一步应用小偏差线性化方法得到了此类系统的线性化模型。针对N个线性化后完全能控的欠驱动Euler—Lagrangian系统，提出了一种同步误差的构造方法，保证了包含N个系统原状态变量和各个系统同步误差信号的增广系统仍然完全能控，进而提出了一种最优同步控制器设计方法。对由两部一级直线倒立摆装置组成的欠驱动Euler—Lagrangian同步运动系统，采用上述方法设计了其最优同步控制器，并在实际的实验设备上进行了实时控制实验。实验结果表明，所提出的最优同步控制器实现了倒立摆装置的稳定平衡和小车位置的精确跟踪，并且令两个装置间达成了同步运动。与主从式同步控制方法相比，此最优同步控制器具有更好的同步效果。

英文摘要：

A partially linearized model for underactuated Euler-Lagrangian systems was obtained based on the feedback linearization method. Then, the small deviation linearization technique was applied to the partially linearized model to obtain a linear model. For N underactuated Euler-Lagrangian systems whose above linearized models were completely controllable, a method to construct the synchronization error signals between the N systems was proposed to guarantee that an augmented system, which contained the original state variables of the N systems and the synchronization errors, was still completely controllable. For the augmented system an optimal synchronization controller was designed. A synchronous motion system composed of two single linear inverted pendulums was used to test the proposed method. The realtime control experimental results show that in the optimal synchronization control system a stable balance of the two inverted pendulums and a precise location of the two cars while they move synchronously have been realized. The effect of the optimal synchronization control scheme is better than the usual masterslave synchronization scheme.