Concurrent synchronization is a regime where diverse groups of fully
synchronized dynamic systems stably coexist. We study global exponential
synchronization and concurrent synchronization in the context of Lagrangian
systems control. In a network constructed by adding diffusive couplings to
robot manipulators or mobile robots, a decentralized tracking control law
globally exponentially synchronizes an arbitrary number of robots, and
represents a generalization of the average consensus problem. Exact nonlinear
stability guarantees and synchronization conditions are derived by contraction
analysis. The proposed decentralized strategy is further extended to adaptive
synchronization and partial-state coupling.

研究在拉格朗日系统控制的背景下，多种全同步的动态系统之间如何稳定地共存，提出了一种基于分散式跟踪控制方法的并发同步解决方案，不仅可以全局指数同步任意数量的机器人，还可以适应机器人的差异实现部分状态耦合，通过收缩分析得出确定的非线性稳定保证和同步条件。