Linying Xiang

Brief paper: Reaching a consensus via pinning control

The consensus problem in a multi-agent system with general nonlinear coupling is investigated in this paper. It is demonstrated that, under suitable conditions on communication, all agents approach a prescribed value if a small fraction of them are controlled by simple feedback control. The stability analysis is based on a blend of graph-theoretic and system-theoretic tools where the contraction analysis and multiple Lyapunov functions play central roles. Numerous numerical examples, which support the analytical results very well, are also included.

Controllability of Weighted and Directed Networks with Nonidentical Node Dynamics

The concept of controllability from control theory is applied to weighted and directed networks with heterogenous linear or linearized node dynamics subject to exogenous inputs, where the nodes are grouped into leaders and followers. Under this framework, the controllability of the controlled network can be decomposed into two independent problems: the controllability of the isolated leader subsystem and the controllability of the extended follower subsystem. Some necessary and/or sufficient conditions for the controllability of the leader-follower network are derived based on matrix theory and graph theory. In particular, it is shown that a single-leader network is controllable if it is a directed path or cycle, but it is uncontrollable for a complete digraph or a star digraph in general. Furthermore, some approaches to improving the controllability of a heterogenous network are presented. Some simulation examples are given for illustration and verification.

Pinning control of complex dynamical networks with heterogeneous delays

Complex dynamical networks with heterogeneous delays in both continuous- and discrete-time domains are controlled by applying local feedback injections to a small fraction of nodes in the whole network. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities (LMI), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to its equilibrium. In some particular cases, a single controller can achieve the control objective. Numerical simulations of various representative networks, including a globally coupled network, a star-coupled network and an Extended Barabasi-Albert (EBA) scale-free network, are finally given for illustration and verification.

Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers

Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogeneous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.

Stabilizing weighted complex networks

Real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections. In this paper, the V-stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics, which includes the unweighted network as a special case. Pinning control is suggested to stabilize such a coupled network. The complicated stabilization problem is reduced to measuring the semi-negative property of the characteristic matrix which embodies not only the network topology, but also the node self-dynamics and the control gains. It is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix. The smaller the second largest eigenvalue is, the more the network is pinning controllable. Numerical simulations of two representative networks composed of non-chaotic systems and chaotic systems, respectively, are shown for illustration and verification.

Finding and evaluating the hierarchical structure in complex networks

A number of recent studies have focused on a statistical property of networked systems—the hierarchical structure. The problem of detecting and characterizing the hierarchical structure has recently attracted considerable attention. In this paper, it is rewritten as optimization in terms of the eigenvalues and eigenvectors. Based on that, an algorithm for reconstructing the hierarchical structure of complex networks is proposed. It is tested on some real-world graphs and is found to offer high sensitivity and reliability.

Coordinated Tracking in Mean Square for a Multi-Agent System With Noisy Channels and Switching Directed Network Topologies

In this brief, a coordinated tracking control problem for a multi-agent system with noisy communication channels is considered under a leader-follower framework. Two control gain functions are designed, where the first one is used to attenuate the noise effect and the second is used to stabilize the system. Using tools from the algebraic graph theory and stochastic analysis, it is proved that, even over a switching directed network topology, the followers can track the leader in mean square.

STABILITY AND CONTROLLABILITY OF ASYMMETRIC COMPLEX DYNAMICAL NETWORKS: EIGENVALUE ANALYSIS

The stability and controllability of asymmetric complex dynamical networks are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the homogenous stationary state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable regions of the coupled network and specifying the eigenvalue distribution of the asymmetric coupling and control matrices. The dependence of the controllability on both pinning density and pinning strength is studied.

Eigenvalue based approach to pinning synchronization in general coupled networks

The synchronization in general coupled networks forced by pinning control is investigated based on eigenvalue analysis. The stable regions for different types of inner coupling links are obtained and the eigenvalue distributions of the coupling and control matrices are analyzed. The effects of network size, weight value of edges, pinning density and pinning strength on the network stability are also tested in numerical studies. It is found that the pinning stability can be improved via increasing the weight of the edges, pinning density and pinning strength for types (i), (iii) and (iv) stable regions, whereas for type (ii) critical curve, too large pinning density and pinning strength will break stable synchronous state.

Distributed output-based self-triggered control for general linear multi-agent systems

This paper addresses the consensus problem via output feedback for a multi-agent system under a distributed self-triggered control framework. A distributed observer-type protocol based on relative output measurements is proposed by incorporating the self-triggered control strategy, where each agent computes its next triggering time based on its local information at the last triggering time. Thus, there is no need to keep track of the measurement errors between two update instants. A simulation example is finally presented to verify the theoretical results.