arXiv subjects

Wenlian Lu

Publications and source records attributed to Wenlian Lu.

At least 73 records · Page 4Linked to original sources

arXiv2015

Global Convergence of Analytic Neural Networks with Event-triggered Synaptic Feedbacks

In this paper, we investigate convergence of a class of analytic neural networks with event-triggered rule. This model is general and include Hopfield neural network as a special case. The event-trigger rule efficiently reduces the frequency of information transmission between synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of its neighbours at its latest triggering time but changes until the next triggering time of this neuron that is determined by certain criterion via its neighborhood information. It is proved that the analytic neural network is completely stable under this event-triggered rule. The main technique of proof is the $Ł$ojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the theoretical results and present the optimisation capability of the network dynamics.

nlin.AO↗

arXiv2015

Pull-Based Distributed Event-triggered Consensus for Multi-agent Systems with Directed Topologies

This paper mainly investigates consensus problem with pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time and the next triggering time of this agent is determined by its in-neighbors' information as well. The general directed topologies, including irreducible and reducible cases, are investigated. The scenario of distributed continuous monitoring is considered firstly, namely each agent can observe its in-neighbors' continuous states. It is proved that if the network topology has a spanning tree, then the event-triggered coupling strategy can realize consensus for the multi-agent system. Then the results are extended to discontinuous monitoring, i.e., self-triggered control, where each agent computes its next triggering time in advance without having to observe the system's states continuously. The effectiveness of the theoretical results are illustrated by a numerical example finally.

math.OC↗

arXiv2015

Distributed Event-triggered Consensus for Multi-agent Systems with Directed Topologies

In this paper, we study consensus problem in multi-agent system with directed topology by event-triggered feedback control. That is, at each agent, the diffusion coupling feedbacks are based on the information from its latest observations to its in-neighbours. We derive distributed criteria to determine the next observation time of each agent that are triggered by its in-neighbours' information and its own states respectively. We prove that if the network topology is irreducible, then under the event-triggered coupling principles, the multi-agent system reach consensus. Then, we extend these results to the case of reducible topology with spanning tree. In addition, these results are also extended to the case of self-triggered control, in terms that the next triggering time of each agent is computed based on the current states, i.e., without observing the system's states continuously. The effectiveness of the theoretical results are illustrated by numerical examples.

nlin.AO↗

arXiv2015

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

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

nlin.AO↗

arXiv2015

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

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.

math.OC↗

arXiv2015

Structure-Based Self-Triggered Consensus in Networks of Multiagents with Switching Topologies

In this paper, we propose a new self-triggered consensus algorithm in networks of multi-agents. Different from existing works, which are based on the observation of states, here, each agent determines its next update time based on its coupling structure. Both centralized and distributed approaches of the algorithms have been discussed. By transforming the algorithm to a proper discrete-time systems without self delays, we established a new analysis framework to prove the convergence of the algorithm. Then we extended the algorithm to networks with switching topologies, especially stochastically switching topologies. Compared to existing works, our algorithm is easier to understand and implement. It explicitly provides positive lower and upper bounds for the update time interval of each agent based on its coupling structure, which can also be independently adjusted by each agent according to its own situation. Our work reveals that the event/self triggered algorithms are essentially discrete and more suitable to a discrete analysis framework. Numerical simulations are also provided to illustrate the theoretical results.

math.OC↗

arXiv2014

Event-triggered Consensus for Multi-agent Systems with Asymmetric and Reducible Topologies

This paper studies the consensus problem of multi-agent systems with asymmetric and reducible topologies. Centralized event-triggered rules are provided so as to reduce the frequency of system's updating. The diffusion coupling feedbacks of each agent are based on the latest observations from its in-neighbors and the system's next observation time is triggered by a criterion based on all agents' information. The scenario of continuous monitoring is first considered, namely all agents' instantaneous states can be observed. It is proved that if the network topology has a spanning tree, then the centralized event-triggered coupling strategy can realize consensus for the multi-agent system. Then the results are extended to discontinuous monitoring, where the system computes its next triggering time in advance without having to observe all agents' states continuously. Examples with numerical simulation are provided to show the effectiveness of the theoretical results.

nlin.AO↗

arXiv2014

A brain-wide association study of DISC1 genetic variants reveals a relationship with the structure and functional connectivity of the precuneus in schizophrenia

The Disrupted in Schizophrenia Gene 1 (DISC1) plays a role in both neural signalling and development and is associated with schizophrenia, although its links to altered brain structure and function in this disorder are not fully established. Here we have used structural and functional MRI to investigate links with six DISC1 single nucleotide polymorphisms (SNPs). We employed a brain-wide association analysis (BWAS) together with a Jacknife internal validation approach in 46 schizophrenia patients and 24 matched healthy control subjects. Results from structural MRI showed significant associations between all six DISC1 variants and gray matter volume in the precuneus, post-central gyrus and middle cingulate gyrus. Associations with specific SNPs were found for rs2738880 in the left precuneus and right post-central gyrus, and rs1535530 in the right precuneus and middle cingulate gyrus. Using regions showing structural associations as seeds a resting-state functional connectivity analysis revealed significant associations between all 6 SNPS and connectivity between the right precuneus and inferior frontal gyrus. The connection between the right precuneus and inferior frontal gyrus was also specifically associated with rs821617. Importantly schizophrenia patients showed positive correlations between the six DISC-1 SNPs associated gray matter volume in the left precuneus and right post-central gyrus and negative symptom severity. No correlations with illness duration were found. Our results provide the first evidence suggesting a key role for structural and functional connectivity associations between DISC1 polymorphisms and the precuneus in schizophrenia.

q-bio.NC↗

arXiv2014

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

In this paper, 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.

math.DS↗

arXiv2014

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 {\em 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.

eess.SY↗

arXiv2014

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 Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially 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, in particular, for the problem of spatial pinning control of network with mobile agents, 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 sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.

eess.SY↗

arXiv2014

New criterion of asymptotic stability for delay systems with time-varying structures and delays

In this paper, we study asymptotic stability of the zero solution of a class of differential systems governed by a scalar differential inequality with time-varying structures and delays. We establish a new generalized Halanay inequality for the asymptotic stability of the zero solution for such systems under more relaxed conditions than the existing ones. We also apply the theoretical results to the analysis of self synchronization in networks of delayed differential systems and obtained a more general sufficient condition for self synchronization.

math.CA↗

arXiv2013

Achieving synchronization in arrays of coupled differential systems with time-varying couplings

In this paper, we study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). The coupling considered here is time-varying in both the network structure and the reaction dynamics. Inspired by our previous paper [6], the extended Hajnal diameter is introduced and used to measure the synchronization in a general differential system. Then we find that the Hajnal diameter of the linear system induced by the time-varying coupling matrix and the largest Lyapunov exponent of the synchronized system play the key roles in synchronization analysis of LCODEs with the identity inner coupling matrix. As an application, we obtain a general sufficient condition guaranteeing directed time-varying graph to reach consensus. Example with numerical simulation is provided to show the effectiveness the theoretical results.

math.DS↗

arXiv2013

Pinning consensus in networks of multiagents via a single impulsive controller

In this paper, we discuss pinning consensus in networks of multiagents via impulsive controllers. In particular, we consider the case of using only one impulsive controller. We provide a sufficient condition to pin the network to a prescribed value. It is rigorously proven that in case the underlying graph of the network has spanning trees, the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals. Interestingly, we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph Laplacian corresponding to the zero eigenvalue and the pinning node we choose. The impulses can be very sparse, with the impulsive intervals being lower bounded. Examples with numerical simulations are also provided to illustrate the theoretical results.

math.OC↗

arXiv2013

Achieving Precise Mechanical Control in Intrinsically Noisy Systems

How can precise control be realised in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way to achieve precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons --trains of Dirac-delta functions-- in biological systems to achieve precise control performance.

math.OC↗

arXiv2013

Spatio-temporal Granger causality: a new framework

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger causality from fMRI, EEG, and other related data.

stat.AP↗

arXiv2013

Cluster consensus in discrete-time networks of multi-agents with inter-cluster nonidentical inputs

In this paper, cluster consensus of multi-agent 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: the intra-cluster synchronization, that the state differences between each pair of agents in the same cluster converge to zero, and inter-cluster separation, that the states of the 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. With them, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then 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, 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.

math.OC↗

arXiv2011

Bifurcations of Emergent Bursting in a Neuronal Network

Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex neuronal network so that we can fully understand the underlying mechanism. Using an oxytocin network developed earlier as an example, we show how we can reduce a complex model with many variables to a tractable model with two variables, while retaining all key qualitative features of the model. The approach enables us to uncover how emergent synchronous bursting could arise from a neuronal network which embodies all known biological features. Surprisingly, the discovered mechanisms for bursting are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multi-time scale spikes: at the membrane potential level and the firing rate level.

q-bio.QM↗