Controllability Ensured Leader Group Selection on Signed Multiagent Networks

Distributed Control of Time-Varying Signed Networks: Theories and Applications

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent's self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks.

Characterizing attitudinal network graphs through frustration cloud

Attitudinal network graphs are signed graphs where edges capture an expressed opinion; two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). A signed graph is called balanced if each of its cycles includes an even number of negative edges. Balance is often characterized by the frustration index or by finding a single convergent balanced state of network consensus. In this paper, we propose to expand the measures of consensus from a single balanced state associated with the frustration index to the set of nearest balanced states. We introduce the frustration cloud as a set of all nearest balanced states and use a graph-balancing algorithm to find all nearest balanced states in a deterministic way. Computational concerns are addressed by measuring consensus probabilistically, and we introduce new vertex and edge metrics to quantify status, agreement, and influence. We also introduce a new global measure of controversy for a given signed graph and show that vertex status is a zero-sum game in the signed network. We propose an efficient scalable algorithm for calculating frustration cloud-based measures in social network and survey data of up to 80,000 vertices and half-a-million edges. We also demonstrate the power of the proposed approach to provide discriminant features for community discovery when compared to spectral clustering and to automatically identify dominant vertices and anomalous decisions in the network.

The Graphical Conditions for Controllability of Multiagent Systems Under Equitable Partition

In this article, by analyzing the eigenvalues and eigenvectors of Laplacian L , we investigate the controllability of multiagent systems under equitable partitions. Two classes of nontrivial cells are defined according to the different numbers of links between them, which are completely connected nontrivial cells (CCNCs) and incompletely connected nontrivial cells. For the system with CCNCs, a necessary condition for controllability is found to be choosing leaders from each nontrivial cell, the number of which should be one less than the cardinality of the cell. It is shown that the controllability is affected by three factors: 1) the number of the links between nontrivial cells; 2) the rank of the connection matrix; and 3) the odevity of the capacity of the nontrivial cells. In the case of nontrivial cells under the equitable partition, there are automorphisms of interconnection graph G , which induce the eigenvectors of L with zero entries. For the system with automorphisms, by taking advantage of the property of eigenvectors associated with L , we propose several graphical necessary conditions for controllability. In addition, by the PBH rank criterion, the controllable subspaces of the system with different classes of nontrivial cells are compared. Finally, a necessary and sufficient condition for controllability under minimum inputs is given.

The Complexity in Complete Graphic Characterizations of Multiagent Controllability

Establishing the graph-based criterion for the selection of any location and any number of leaders is the main difficulty in the complete graphic characterization of multiagent controllability. This greatly increases the complexity of the study, compared with the results derived for only one or several classes of leaders. Through a detailed analysis of graphs of six nodes, this article presents a systematic design and identification process for the complete graphic characterization by taking advantage of controllability destructive nodes. The topologies obtained by the proposed method allow directly determining controllability at the network topology level. The results are not only applicable to any leader's selection but also reveal the difficulty and complexity in the study of complete controllability graphic characterizations. Moreover, by comparing graphs composed of five and six nodes, the results reveal the graph-theory-based controllability complexity caused by adding only one node. Finally, results are derived to show how to design topology structures to ensure the controllability under any selection of leaders.