Identifying the Most Influential Driver Nodes for Pinning Control of Multi-Agent Systems with Time-Varying Topology
Guangrui Zhang, Zhaohui Liu, Xinghuo Yu, Mahdi Jalili
TL;DR
The paper tackles identifying the most influential driver nodes for fastest synchronization in multi-agent systems with time-varying topologies. It introduces a periodic-switching framework and analyzes stability through the transition matrix, defining a speed metric $b_{T,i}=(1/T)\ln \rho(R_{T,i}(T))$ to rank driver nodes. A key theoretical result shows the driver-node choice can be independent of the system matrix $A$ when the inner coupling matrix $\Lambda=I$, and it provides a switching-frequency threshold $T_0$ ensuring the average-system winner remains optimal for small periods. Numerical simulations on a four-node network validate the theory, demonstrating the fastest synchronization when the identified driver node is pinned and illustrating the practical impact of switching dynamics on node selection.
Abstract
Identifying the most influential driver nodes to guarantee the fastest synchronization speed is a key topic in pinning control of multi-agent systems. This paper develops a methodology to find the most influential pinning nodes under time-varying topologies. First, we provide the pinning control synchronization conditions of multi-agent systems. Second, a method is proposed to identify the best driver nodes that can guarantee the fastest synchronization speed under periodically switched systems. We show that the determination of the best driver nodes is independent of the system matrix under certain conditions. Finally, we develop a method to estimate the switching frequency threshold that can make the selected best driver nodes remain the same as the average system. Numerical simulations reveal the feasibility of these methods.