Target Controllability of Multiagent Systems under Directed Weighted Topology

TL;DR

This paper investigates the conditions for target controllability in multiagent systems with directed weighted graphs, providing necessary and sufficient criteria, a target node selection method, and extending results to high-order systems and general linear systems.

Contribution

It introduces a graph partition-based approach to characterize target controllability and offers a target node selection method, extending the analysis to high-order and general linear systems.

Findings

System is target controllable if each cell has at most one target node.

No unreachable target nodes exist in the system.

Target controllability of high-order systems matches that of first-order systems under fixed topology, leaders, and targets.

Abstract

In this paper, the target controllability of multiagent systems under directed weighted topology is studied. A graph partition is constructed, in which part of the nodes are divided into different cells, which are selected as leaders. The remaining nodes are divided by maximum equitable partition. By taking the advantage of reachable nodes and the graph partition, we provide a necessary and sufficient condition for the target controllability of a first-order multiagent system. It is shown that the system is target controllable if and only if each cell contains no more than one target node and there are no unreachable target nodes, with $\delta-$reachable nodes belonging to the same cell in the above graph partition. By means of controllability decomposition, a necessary and sufficient condition for the target controllability of the system is given, as well as a target node selection method to ensure the target controllability. In a high-order multiagent system, once the topology, leaders, and target nodes are fixed, the target controllability of the high-order multiagent system is shown to be the same to the first-order one. This paper also considers a general linear system. If there is an independent strongly connected component that contains only target nodes and the general linear system is target controllable, then graph $\mathcal{G}$ is leader-target follower connected.