Abstract
In this article, the convergence speed and robustness of the consensus for several dual-layered star-composed multi-agent networks are studied through the method of graph spectra. The consensus-related indices, which can measure the performance of the coordination systems, refer to the algebraic connectivity of the graph and the network coherence. In particular, graph operations are introduced to construct several novel two-layered networks, the methods of graph spectra are applied to derive the network coherence for the multi-agent networks, and we find that the adherence of star topologies will make the first-order coherence of the dual-layered systems increase some constants in the sense of limit computations. In the second-order case, asymptotic properties also exist when the index is divided by the number of leaf nodes. Finally, the consensus-related indices of the duplex networks with the same number of nodes but non-isomorphic structures have been compared and simulated, and it is found that both the first-order coherence and second-order coherence of the network D are between A and B, and C has the best first-order robustness, but it has the worst robustness in the second-order case.
Highlights
Consensus is a class of distributed coordination problems of multi-agent systems, and the essence of the problem is that all agents are required to achieve a common state value under some given control strategies
To solve the consensus problems, the linking structure among agents is always interpreted by the communication graph of the system, and the performance indices of consensus models, such as convergence speed [1, 8] and network coherence [10,11,12,13,14], can be characterized by the Laplacian
As we mentioned in the Introduction part, the layered starlike networks of this paper are a kind of network in which all nodes have identical dynamics, and they have the topology composed by linking the center nodes among the basic star topologies
Summary
Consensus is a class of distributed coordination problems of multi-agent systems, and the essence of the problem is that all agents are required to achieve a common state value under some given control strategies. To solve the consensus problems, the linking structure among agents is always interpreted by the communication graph of the system, and the performance indices of consensus models, such as convergence speed [1, 8] and network coherence [10,11,12,13,14], can be characterized by the Laplacian. Synchronization problems, which share similar control strategies and have the same essence as consensus problems, are always connected with the network structure [19,20,21,22,23,24] and are studied from the angle of graph theory
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