Analysis of distributed consensus protocols with multi-equilibria under time-delays

Topology design for group consensus in directed multi-agent systems

“…As can be seen from the figure, the multi-agent network forms 8 groups where the agents in the same group gather at the same location. While it is not straightforward to directly conclude these groups from the structure of the network (see Figure 1), the groups and their members can be determined by utilizing the definitions of primary and secondary layer subgraphs which were first introduced in [10] and restated in Definition 2.5. Remark 2.4.…”

“…Definition 2.5. (Primary and secondary layer subgraphs Erkan et al [10]) A directed graph, G = (V, E), can be uniquely partitioned into…”

“…However, for the secondary layer subgraphs, there is a unique root that receives information from the rest of the graph which we call the principal root of the subgraph and denote by r Gs,j . Note here that with the above definition, each vertex in G will either be in a primary or a secondary layer subgraph and these subgraphs can be uniquely determined [9,10]. Note also that an isolated vertex is a primary layer subgraph itself by definition.…”

“…In this case, the agents in a group achieve consensus with the agents in the same group DOI: 10.14736/kyb-2020- whereas the agreement values of the groups are different. Although the number of groups is equal to the number of connected components in an undirected network, as we have shown in our previous study, the graph structure must be exploited in order to determine the number of groups in a directed network [10]. Since there are important applications of group consensus in multi-agent systems (e. g., groups with different opinions in social networks, containment control of multi-robot networks), the problem of topology design for group consensus needs to be properly addressed.…”

“…In [10], we have introduced the novel concepts of primary and secondary layer subgraphs 1 that are further utilized to express the number of groups to be formed. It is also shown that agents in a particular subgraph achieve consensus with the agents in the same group, i. e., one can determine the total number of groups and the agents in each group in a multi-agent network with directed topology by using these concepts.…”