Haibin Shao

Aggregation stability of multiple agents with general nonlinear attraction and repulsion forces

In this paper we consider the aggregation stability problem of a multi-agents system under network, among the agents there are nonlinear attactive/repulsive forces. Our work generalizes the results given by Gazi and Passino [1] and Chu, Wang and Chen [2], [3], [4] into a very general setting. It shows that the agents of multi-agents system in undirect communication network will asymptotically form a cohesive cluster with finite size if the nonlinear attraction and repulsion functions satisfy some very mild assumptions. We give several numerical simulations demonstrate that the collective behavior of system appear stable cohesion with finite size cohesive areas if the mild assumption is satisfied. We also study the system with directed networks. In such cases the swarms with same nonlinear attactive/repulsive forces may exhibit oscillation and dispersal phenomenon.

Consensus problem of second-order multi-agent system in directed network: A matrix analysis approach

In this paper the consensus of multi-agent system in directed network, where the agent is described by a second-order dynamics, is studied. The control protocol depends on two parameters, i.e. position-cooperative parameter wx >0 and velocity-cooperation parameter wv >0, and the Laplacian associated with communication network. The definition of consensus in this paper is slightly different from that used in some existent literature. We define the notion called inertia-consensus. Based on a matrix decomposition of the Laplacian, we define the notions called basic independent system and basic non-independent system of a multi-agent system under directed networks. Furthermore, using matrix analysis approach the necessary and sufficient conditions for state inertia-consensus and/or velocity inertia-consensus, are given for the second-order systems. Also, the collective behavior of the system is discussed subject to the cases that system achieves consensus or does not. We also provide some simulation results to show the validation of our results.

Laplacian dynamics on signed networks

In this paper, we examine the properties of the Laplacian matrix defined on signed networks, referred to as the signed Laplacian matrix, from a graph-theoretic perspective. The connection between the stability of the signed Laplacian with the cut set of the network is established. This is then followed by relating and the number of negative eigenvalues of the signed Laplacian to the number of negatively weighted edges in the network. In order to stabilize the signed Laplacian dynamics, a distributed diagonal compensation approach is proposed; we show that this compensation is closely related to the structural balance of the network. Furthermore, the influence of the external input exerted on the signed Laplacian dynamics is investigated.

Verification and prediction of structural balance: A data-driven perspective

The structural balance plays a fundamental role in networked systems with both attractive and repulsive interactions, which can be characterized by a signed network. In this paper, we show that the ensemble of type of interaction in a signed network can be inferred from the eigenvector of the signed Laplacian matrix. Also, it has been shown that a graph, derived from the graph Cartesian product of factor graphs, is structurally balanced if and only if its factors are structurally balanced. According to the theoretical results, the verification and prediction of the structural balance of the signed network is presented from a data-driven perspective by utilizing the dynamic mode decomposition.

A data-driven approach for influencing consensus networks

In this paper, we examine data-driven aspects of consensus networks influenced by a stubborn agent. In particular we show that the judicious placement of the stubborn agent can be achieved based on snapshots of the data generated by the network through estimating the appropriate eigenvector of the perturbed Laplacian matrix. The exact dynamic mode decomposition algorithm is employed for estimating the spectral properties of the network and we show that the dominant eigenvector can be determined if the rank of data snapshots is equal to the number of eigenvalue clusters of the perturbed Laplacian. Lastly, for large-scale networks, we provide a simple data-driven algorithm for approximating the spectral properties of the network.

Inferring Centrality from Network Snapshots

The topology and dynamics of a complex network shape its functionality. However, the topologies of many large-scale networks are either unavailable or incomplete. Without the explicit knowledge of network topology, we show how the data generated from the network dynamics can be utilised to infer the tempo centrality, which is proposed to quantify the influence of nodes in a consensus network. We show that the tempo centrality can be used to construct an accurate estimate of both the propagation rate of influence exerted on consensus networks and the Kirchhoff index of the underlying graph. Moreover, the tempo centrality also encodes the disturbance rejection of nodes in a consensus network. Our findings provide an approach to infer the performance of a consensus network from its temporal data.

On the fiedler vector of graphs and its application in consensus networks

In this paper, we examine the influence of the normalized eigenvectors of the graph Laplacian matrix on the behavior of individual agents undergoing consensus dynamics. We show that the Fielder vector can be estimated from the states of the agents and that the entries of this vector can describe the subsequent behavior of the agents. In addition, we discuss how the Fiedler vector sheds light on the energy damping rate of the consensus network driven by unit impulse. As an application, we show that the characteristic set of a graph can be identified based on the corresponding Fiedler vector.

On the degree of synchrony

In this paper, we introduce a measure quantifying the degree of synchrony for consensus networks in terms of the angle between the network state vector and the agreement subspace of ℝn. The desynchronization of a consensus network is then examined by adopting a simple two-stubborn-input strategy, through which the network synchrony can be alleviated when the inputs are symmetric with respect to the origin. In particular, for tree graphs, we show that the proposed measure of synchrony is characterized by the so-called backbone path and can be computed efficiently by examining graph-theoretic properties of the network.