Convergence time and speed of multi-agent systems in noisy environments

On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters-From the Perspective of Cardinalities of Vertex Sets

This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system's robustness. Graph operations are applied to design the novel multi-layered networks, and a graph spectrum approach, along with analysis methods, is applied to derive the mathematical expression of the coherence, and the corresponding asymptotic results on the performance index have been obtained. In addition, the coherence of these non-isomorphic multi-layered networks with three different graph parameters are compared and analyzed. We find that, when the cardinalities of the vertex sets of corresponding counterpart layers are the same, the multi-layered topology class with a balanced, complete, multi-partite structure has the best robustness of all the considered networks, if the sufficient conditions for the node-related parameters hold. Finally, simulations are given to verify the asymptotic results.

Consensus-Related Performance of Triplex MASs Based on Partial Complete Graph Structure

This article mainly studies first-order coherence related to the robustness of the triplex MASs consensus models with partial complete graph structures; the performance index is studied through algebraic graph theory. The topologies of the novel triplex networks are generated by graph operations and the approach of graph spectra is applied to calculate the first-order network coherence. The coherence asymptotic behaviours of the three cases of the partial complete structures are analysed and compared. We find that under the condition that the number of nodes in partial complete substructures n tends to infinity, the coherence asymptotic behaviour of the two sorts of non-isomorphic three-layered networks will be increased by r-12(r+1), which is irrelevant to the peripheral vertices number p; when p tends to infinity, adding star copies to the original triplex topologies will reverse the original size relationship of the coherence under consideration of the triplex networks. Finally, the coherence of the three-layered networks with the same sorts of parameters, but non-isomorphic graphs, are simulated to verify the results.

On Consensus Indices of Triplex Multiagent Networks Based on Complete k-Partite Graph

In this article, the performance indices on consensus problems for three-layered, multiagent systems are studied from the perspective of algebraic graph theory, where the indices can be used as a measurement of the system performance and refer to the network coherence and algebraic connectivity. Specifically, some operations of two graphs are applied to established the three-layered networks based on k-partite structure, and the mathematical expression of the coherence is derived by the methods of algebraic graph theory. We found that the operations of adding star-shaped copies or fan-graph copies will make the coherence increase by some scalars under the computations of limitation. Then, the indices of the three-layered systems with non-isomorphic topologies but the same number of nodes were compared and simulated; it is found that, when the number of nodes in the counterpart node classes tend to infinity, their difference in coherence are only relevant with the number of peripheral nodes in the sense of limitation.

Finite-time flocking with collision-avoiding problem of a modified Cucker-Smale model

To achieve collision-avoiding flocking in finite time, a modified Cucker-Smale model with general inter-driving force is proposed. First, it is proved that the system can achieve conditional collision-avoiding flocking in finite time by imposing appropriate restrictions on the initial states. Moreover, a special case of the inter-driving force is demonstrated. Last, the correctness of the results is verified through numerical simulations.

On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach

In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results.

Realization of consensus of multi-agent systems with stochastically mixed interactions

In this paper, we propose a new consensus model in which the interactions among agents stochastically switch between attraction and repulsion. Such a positive-and-negative mechanism is described by the white-noise-based coupling. Analytic criteria for the consensus and non-consensus in terms of the eigenvalues of the noise intensity matrix are derived, which provide a better understanding of the constructive roles of random interactions. Specifically, we discover a positive role of noise coupling that noise can accelerate the emergence of consensus. We find that the converging speed of the multi-agent network depends on the square of the second smallest eigenvalue of its graph Laplacian. The influence of network topologies on the consensus time is also investigated.