Design of consensus and cluster consensus controller for first-order nonlinear multi-agent systems based on subgroup structure

• Published in: Neurocomputing (Amsterdam) Vol. 600; p. 128141
• Main Authors: Wang, Yi, Ma, Zhongjun, Chen, Guoyuan, Cao, Jinde
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2024
• Subjects: Cluster consensus; Lipschitz condition; Multi-agent system; Nonlinear dynamics; Cluster consensus; Nonlinear dynamics; Lipschitz condition; Multi-agent system
• ISSN: 0925-2312
• DOI: 10.1016/j.neucom.2024.128141

It is well known that nonlinear multi-agent systems (MASs) with a directed topology can reach a consensus if the global coupling coefficient is strong enough. In this paper, we propose a novel distributed protocol based on the subgroup structure. Our results demonstrate that the MAS design can follow a part-to-whole approach, starting with subgroups and gradually building up to a more complex system. We firstly consider two cases for the MASs: one with a single leader and one with a leader group, where agents within the leader group can communicate with each other, but cannot receive the information of other group. We show that followers can track the leader or group leaders if intra-coupling within the subgroup and information strength received by the root node are above a certain threshold. Next, we investigate cluster consensus and practical cluster consensus for the Laplacian matrix with unequal row sum, equal row sum, and mixing of partitioned matrices. Our results reveal that row sum and community structure of the partitioned matrix are crucial in determining the final state of each agent. Our proposed control protocol is highly flexible and relies only on the cluster structure and information received by the root node, rather than global information. Moreover, our method is not limited to tracking problems, cooperative control, or multi-objective control, and can accommodate new group agents joining the system, making it highly adaptable. We provide illustrative examples to demonstrate the effectiveness of our approach.