旋转矩阵列同步的动态控制器：一种QR分解方法
Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach
AI总结：
本文提出基于QR分解的动态控制器，用于多智能体系统中旋转矩阵列的同步问题，通过引入辅助变量实现动态控制，实现准强交互图拓扑下的近全局收敛。
摘要：
在多智能体系统中，本文研究了连续时间分布式旋转矩阵列同步问题。具体而言，k个特定列需同步，仅假设可用k个相对旋转列进行控制设计。当考虑单个列时，问题等价于在(d-1)维单位球上的同步；当考虑所有列时，问题等价于在SO(d)上的同步。本文设计了动态控制律，基于引入辅助变量与QR分解方法。QR分解方法的优势在于可将k列的动力学与剩余d-k列的动力学解耦。在该控制方案下，闭环系统在准强交互图拓扑下实现近全局收敛到同步。
英文摘要：
In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d-1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the k columns from the remaining d-k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies.
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