[1]ZHAO Huihui,JI Zhijian.Symbolic network controllability based on a consistency protocol under distance division[J].CAAI Transactions on Intelligent Systems,2025,20(5):1178-1187.[doi:10.11992/tis.202405038]
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Symbolic network controllability based on a consistency protocol under distance division

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 20 Number of periods: 2025 5 Page number: 1178-1187 Column: 学术论文—智能系统 Public date: 2025-09-05
Title:
Symbolic network controllability based on a consistency protocol under distance division
Author(s):
ZHAO Huihui;  JI Zhijian
School of Automation, Qingdao University, Qingdao 266071, China
Keywords:
multiagent network; distance division; undirected signed network; controllability; leader-follower framework; eigenvalue; eigenvector; control theory
CLC:
TP273
DOI:
10.11992/tis.202405038
Abstract:
The controllability of symbolic networks in general linear multiagent systems is explored in this study. First, two distinct leader-follower models are analyzed, highlighting and clarifying the differences in their expressions. Next, building on the above-mentioned models, the controllable subspace of the network is quantitatively described from the perspective of network topology, utilizing the distance division tool introduced here for the first time. Inspired by distance division, conditions for K-controllability were obtained (K-controllability means that the control signal can reach all nodes within K steps, where K corresponds to the system’s controllability index). For dense network topologies with complex structures, a novel algorithm is proposed for calculating the system’s K value. By adopting a graph theory approach, the algorithm leverages operations such as traversing and trimming edges of the topology graph. This approach circumvents the need for complex matrix calculations used in traditional methods while also providing a method for leader selection. Finally, the validity of the algorithm is demonstrated through practical examples.
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