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Abstract: This article investigates the controllability problem of multi-agent systems. Each agent is assumed to be governed by a second-order consensus control law corresponding to a directed and weighted graph. Two types of topology are considered. The first is concerned with directed trees, which represent the class of topology with minimum information exchange among all controllable topologies. A very simple necessary and sufficient condition regarding the weighting scheme is obtained for the controllability of double integrator multi-agent systems in this scenario. The second is concerned with a more general graph that can be reduced to a directed tree by contracting a cluster of nodes to a component. A similar necessary and sufficient condition is derived. Finally, several illustrative examples are provided to demonstrate the theoretical analysis results.

This paper proposes a method to choose weights in a directed graph that models a leader-follower network of double integrators so that the network is controllable. The proposed condition which basically consists in choosing different weights for each link is proven to be necessary and sufficient. The authors also consider contracted-trees, which slightly generalize the result to graphs in which nodes can clustered so that a directed tree connects the clusters and inside the clusters there can be arbitrary feedback links among nodes of the same cluster. The paper is well written and clear. The results seem technically sound.

基于有向权重拓扑的二阶多智能体系统可控性分析

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