Yujuan Han

Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs

In this paper, cluster consensus of multiagent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: intracluster synchronization, the state at which differences between each pair of agents in the same cluster converge to zero, and inter-cluster separation, the state at which agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus, including the spanning trees, scramblingness, infinite stochastic matrix product, and Hajnal inequality, are extended. As a result, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then the static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T > 0 such that the union graph across any T-length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified non-Bayesian social learning model to illustrate the effectiveness of our results.

Achieving Cluster Consensus in Continuous-Time Networks of Multi-Agents With Inter-Cluster Non-Identical Inputs

In this technical note, cluster consensus in continuous-time networks of multi-agents with time-varying topologies via non-identical inter-cluster inputs is studied. The cluster consensus contains two aspects: intra-cluster synchronization, that the state differences between agents in the same cluster converge to zero, and inter-cluster separation, that the states of the agents in different clusters do not approach. δ-cluster-spanning-tree in continuous-time networks of multi-agent systems plays essential role in analysis of cluster synchronization. Inter-cluster separation can be realized by imposing adaptive inputs that are identical within the same cluster but different in different clusters, under the inter-cluster common influence condition. Simulation examples demonstrate the effectiveness of the derived theoretical results.

Synchronization in Networks of Linearly Coupled Dynamical Systems via Event-Triggered Diffusions

In this paper, we utilize event-triggered coupling configurations to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes and their neighborhood and the next observation time is triggered by the proposed criteria based on the local neighborhood information as well. Two scenarios are considered: 1) continuous monitoring, in which each node can observe its neighborhoods instantaneous states and 2) discrete monitoring, in which each node can obtain only its neighborhoods states at the same time point when the coupling term is triggered. In both the cases, we prove that if the system with persistent coupling can synchronize, then these event-triggered coupling strategies can synchronize the system too.

Characterizing the power of moving target defense via cyber epidemic dynamics

Moving Target Defense (MTD) can enhance the resilience of cyber systems against attacks. Although there have been many MTD techniques, there is no systematic understanding and quantitative characterization of the power of MTD. In this paper, we propose to use a cyber epidemic dynamics approach to characterize the power of MTD. We define and investigate two complementary measures that are applicable when the defender aims to deploy MTD to achieve a certain security goal. One measure emphasizes the maximum portion of time during which the system can afford to stay in an undesired configuration (or posture), without considering the cost of deploying MTD. The other measure emphasizes the minimum cost of deploying MTD, while accommodating that the system has to stay in an undesired configuration (or posture) for a given portion of time. Our analytic studies lead to algorithms for optimally deploying MTD.

Pinning networks of coupled dynamical systems with Markovian switching couplings and event-triggered diffusions

Abstract In this paper, stability of linearly coupled dynamical systems with feedback pinning algorithm is studied. Here, both the coupling matrix and the set of pinned-nodes vary with time, induced by a continuous-time Markov chain with finite states. Event-triggered rules are employed on both diffusion coupling and feedback pinning terms, which can efficiently reduce the computation load, as well as communication load in some cases and be realized by the latest observations of the state information of its local neighborhood and the target trajectory. The next observation is triggered by certain criterion (event) based on these state information as well. Two scenarios are considered: the continuous monitoring, that each node observes the state information of its neighborhood and target (if pinned) in an instantaneous way, to determine the next triggering event time, and the discrete monitoring, that each node needs only to observe the state information at the last event time and predict the next triggering-event time. In both cases, we present several event-triggering rules and prove that if the conditions that the coupled system with persistent coupling and control can be stabilized are satisfied, then these event-trigger strategies can stabilize the system, and Zeno behaviors are excluded in some cases. Numerical examples are presented to illustrate the theoretical results.

Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller–node set. Here, the coupling matrices and the controller–node sets change with time, induced by a continuous-time Markov chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponential stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller–node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable subsystems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.

Consensus analysis of networks with time-varying topology and event-triggered diffusions

This paper studies the consensus problem of networks with time-varying topology. Event-triggered rules are employed in diffusion coupling terms to reduce the updating load of the coupled system. Two strategies are considered: event-triggered strategy, that each node observes the state information in an instantaneous way, to determine the next triggering event time, and self-triggered strategy, that each node only needs to observe the state information at the event time to predict the next triggering event time. In each strategy, two kinds of algorithms are considered: the pull-based algorithm, that the diffusion coupling term of every node is updated at the latest observations of the neighborhood at its triggered time, and push-based algorithm, the diffusion coupling term of every node uses the state information of its neighborhood at their latest triggered time. It is proved that if the coupling matrix across time intervals with length less than some given constant has spanning trees, then the proposed algorithms can realize consensus. Examples with numerical simulation are provided to show the effectiveness of the theoretical results.

Cluster consensus of networks of second-order multi-agent systems with inter-cluster non-identical inputs

This paper studies the second order cluster consensus problem for a network of multi-agents. We consider general graph topologies including time variation. A comprehensive analysis is provided. For static topology case, we show that communications among agents and inter-cluster nonidentical inputs generically leads the system to second order cluster consensus. A common Lyapunov function is provided for time varying topologies case. Numerical simulation results demonstrate that the second order cluster consensus can be achieved using the proposed algorithms.

Achieving cluster consensus in continuous-time networks of multi-agents with adapted inputs

In this paper, cluster consensus problem in continuous-time networks of multi-agents with external inputs is studied. Here, following [29], cluster consensus is defined in two aspects: intra-cluster synchronization, which means that the state differences among agents in the same cluster asymptotically converge to zero, and inter-cluster separation, which means the states of the agents in different clusters are separated. Under the inter-cluster common influence condition and with adapted inter-cluster identical inputs, the stability of cluster consensus is proved by extending the existing concepts and approaches in the matrix and graph theories to the cluster cases. The adapted inputs are also required to separate different clusters (or called inter-cluster separation). For the graph of the network, both static and switching topologies are considered. Numerical simulation to verify the theoretical results is given, too.

Pinning dynamic complex networks by time-varying controller-vertex set

In this paper, we give a stability analysis of multi-agent system with a local pinning control algorithm for very general network topologies. These include determinately directed time varying topologies, the stochastically switching topologies. The pinned vertex set also varies with time, including deterministic and stochastic time-variations. We present sufficient conditions to guarantee the convergence of the pinning process: for the deterministic case, a time-varying pinned vertex set can stabilize the network of multi-agents with time-varying topologies if any vertex in the networks can be accessed by directed paths by at least one vertex in the pinned vertex set across all time intervals that are pre-defined; Similar results are also given for the stochastically switching case. As applications, numerical simulations based on the random waypoint model are given to verify our theoretical results.