Influencer identification of dynamical networks based on an information entropy dimension reduction method

Identifying critical nodes or sets in large-scale networks is a fundamental scientific problem and one of the key research directions in the fields of data mining and network science when implementing network attacks, defense, repair and control.Traditional methods usually begin from the centrality, node location or the impact on the largest connected component after node destruction, mainly based on the network structure.However, these algorithms do not consider network state changes.We applied a model that combines a random connectivity matrix and minimal low-dimensional structures to represent network connectivity.By using mean field theory and information entropy to calculate node activity,we calculated the overlap between the random parts and fixed low-dimensional parts to quantify the influence of node impact on network state changes and ranked them by importance.We applied this algorithm and the proposed importance algorithm to the overall analysis and stratified analysis of the C.elegans neural network.We observed a change in the critical entropy of the network state and by utilizing the proposed method we can calculate the nodes that indirectly affect muscle cells through neural layers.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

Spontaneous Recovery in Directed Dynamical Networks

Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneously return to normal after a seizure,and traffic flow can become smooth again after a jam.Previous studies on the spontaneous recovery of dynamical networks have been limited to undirected networks.However,most real-world networks are directed.To fill this gap,we build a model in which nodes may alternately fail and recover,and we develop a theoretical tool to analyze the recovery properties of directed dynamical networks.We find that the tool can accurately predict the final fraction of active nodes,and the prediction accuracy decreases as the fraction of bidirectional links in the network increases,which emphasizes the importance of directionality in network dynamics.Due to different initial states,directed dynamical networks may show alternative stable states under the same control parameter,exhibiting hysteresis behavior.In addition,for networks with finite sizes,the fraction of active nodes may jump back and forth between high and low states,mimicking repetitive failure-recovery processes.These findings could help clarify the system recovery mechanism and enable better design of networked systems with high resilience.

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.

SYNCHRONIZATION OF MASTER-SLAVE MARKOVIAN SWITCHING COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING MODE CONTROL

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Topology identification for a class of complex dynamical networks using output variables

A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.

Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control

In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node＇s state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.

A Dynamic-Bayesian-Networks-Based Resilience Assessment Approach of Structure Systems: Subsea Oil and Gas Pipelines as A Case Study

Under unanticipated natural disasters, any failure of structure components may cause the crash of an entire structure system. Resilience is an important metric for the structure system. Although many resilience metrics and assessment approaches are proposed for engineering system, they are not suitable for complex structure systems, since the failure mechanisms of them are different under the influences of natural disasters. This paper proposes a novel resilience assessment metric for structure system from a macroscopic perspective, named structure resilience, and develops a corresponding assessment approach based on remaining useful life of key components. Dynamic Bayesian networks(DBNs) and Markov are applied to establish the resilience assessment model. In the degradation process, natural degradation and accelerated degradation are modelled by using Bayesian networks, and then coupled by using DBNs. In the recovery process, the model is established by combining Markov and DBNs. Subsea oil and gas pipelines are adopted to demonstrate the application of the proposed structure metric and assessment approach.

Disturbance rejection and H_∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

Fault diagnosis of time-delay complex dynamical networks using output signals

This paper proposes a novel approach for fault diagnosis of a time-delay complex dynamical network. Unlike the other methods, assuming that the dynamics of the network can be described by a linear stochastic model, or using the state variables of nodes in the network to design an adaptive observer, it only uses the output variable of the nodes to design an observer and an adaptive law of topology matrix in the observer of a complex network, leading to simple design of the observer and easy realisation of topology monitoring for the complex networks in real engineering. The proposed scheme can monitor any changes of the topology structure of a time-delay complex network. The effectiveness of this method is successfully demonstrated by virtue of a complex networks with Lorenz model.

Successive lag synchronization on dynamical networks with communication delay

In this paper, successive lag synchronization （SLS） on a dynamical network with communication delay is investigated. In order to achieve SLS on the dynamical network with communication delay, we design linear feedback control and adaptive control, respectively. By using the Lyapunov function method, we obtain some sufficient conditions for global stability of SLS. To verify these results, some numerical examples are further presented. This work may find potential applications in consensus of multi-agent systems.

Stochastic synchronization for time-varying complex dynamical networks

This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.

Comparison of dynamic Bayesian network approaches for online diagnosis of aircraft system

The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To address this problem, two dynamic Bayesian network(DBN) approaches are proposed. One approach prunes the DBN of system, and then uses particle filter(PF) for this pruned DBN(PDBN) to perform online diagnosis. The problem is that estimates from a PF tend to have high variance for small sample sets. Using large sample sets is computationally expensive. The other approach compiles the PDBN into a dynamic arithmetic circuit(DAC) using an offline procedure that is applied only once, and then uses this circuit to provide online diagnosis recursively. This approach leads to the most computational consumption in the offline procedure. The experimental results show that the DAC, compared with the PF for PDBN, not only provides more reliable online diagnosis, but also offers much faster inference.

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.

New Synchronization Algorithm and Analysis of Its Convergence Rate for Clock Oscillators in Dynamical Network with Time-Delays

New synchronization algorithm and analysis of its convergence rate for clock oscillators in dynamical network with time-delays are presented.A network of nodes equipped with hardware clock oscillators with bounded drift is considered.Firstly,a dynamic synchronization algorithm based on consensus control strategy,namely fast averaging synchronization algorithm （FASA）,is presented to find the solutions to the synchronization problem.By FASA,each node computes the logical clock value based on its value of hardware clock and message exchange.The goal is to synchronize all the nodes＇ logical clocks as closely as possible.Secondly,the convergence rate of FASA is analyzed that proves it is related to the bound by a nondecreasing function of the uncertainty in message delay and network parameters.Then,FASA＇s convergence rate is proven by means of the robust optimal design.Meanwhile,several practical applications for FASA,especially the application to inverse global positioning system （IGPS） base station network are discussed.Finally,numerical simulation results demonstrate the correctness and efficiency of the proposed FASA.Compared FASA with traditional clock synchronization algorithms （CSAs）,the convergence rate of the proposed algorithm converges faster than that of the CSAs evidently.

Fault Tolerant Synchronization for a General Complex DynamicalNetwork with Random Delay

A fault tolerant synchronization strategy is proposed to synchronize a complex network with random time delays and sensor faults. Random time delays over the network transmission are described by using Markov chains. Based on the Lyapunov stability theory and stochastic analysis, several passive fault tolerant synchronization criteria are derived,which can be described in the form of linear matrix inequalities. Finally,a numerical simulation example is carried out and the results show the validity of the proposed fault tolerant synchronization controller.

Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network

This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays. Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations, as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks. It is shown that, through Lyapunov stability theory, distributed adaptive controllers con- structed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks, and perturbation inputs. A Chua＇s circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.

Image super‐resolution via dynamic network

Convolutional neural networks depend on deep network architectures to extract accurate information for image super‐resolution.However,obtained information of these con-volutional neural networks cannot completely express predicted high‐quality images for complex scenes.A dynamic network for image super‐resolution(DSRNet)is presented,which contains a residual enhancement block,wide enhancement block,feature refine-ment block and construction block.The residual enhancement block is composed of a residual enhanced architecture to facilitate hierarchical features for image super‐resolution.To enhance robustness of obtained super‐resolution model for complex scenes,a wide enhancement block achieves a dynamic architecture to learn more robust information to enhance applicability of an obtained super‐resolution model for varying scenes.To prevent interference of components in a wide enhancement block,a refine-ment block utilises a stacked architecture to accurately learn obtained features.Also,a residual learning operation is embedded in the refinement block to prevent long‐term dependency problem.Finally,a construction block is responsible for reconstructing high‐quality images.Designed heterogeneous architecture can not only facilitate richer structural information,but also be lightweight,which is suitable for mobile digital devices.Experimental results show that our method is more competitive in terms of performance,recovering time of image super‐resolution and complexity.The code of DSRNet can be obtained at https://github.com/hellloxiaotian/DSRNet.

Hash function construction using weighted complex dynamical networks

A novel scheme to construct a hash function based on a weighted complex dynamical network （WCDN） generated from an original message is proposed in this paper. First, the original message is divided into blocks. Then, each block is divided into components, and the nodes and weighted edges are well defined from these components and their relations. Namely, the WCDN closely related to the original message is established. Furthermore, the node dynamics of the WCDN are chosen as a chaotic map. After chaotic iterations, quantization and exclusive-or operations, the fixed-length hash value is obtained. This scheme has the property that any tiny change in message can be diffused rapidly through the WCDN, leading to very different hash values. Analysis and simulation show that the scheme possesses good statistical properties, excellent confusion and diffusion, strong collision resistance and high efficiency.

Remaining Useful Life Prediction Method for Multi-Component System Considering Maintenance:Subsea Christmas Tree System as A Case Study

Maintenance is an important technical measure to maintain and restore the performance status of equipment and ensure the safety of the production process in industrial production,and is an indispensable part of prediction and health management.However,most of the existing remaining useful life(RUL)prediction methods assume that there is no maintenance or only perfect maintenance during the whole life cycle;thus,the predicted RUL value of the system is obviously lower than its actual operating value.The complex environment of the system further increases the difficulty of maintenance,and its maintenance nodes and maintenance degree are limited by the construction period and working conditions,which increases the difficulty of RUL prediction.An RUL prediction method for a multi-omponent system based on the Wiener process considering maintenance is proposed.The performance degradation model of components is established by a dynamic Bayesian network as the initial model,which solves the uncertainty of insufficient data problems.Based on the experience of experts,the degree of degradation is divided according to Poisson process simulation random failure,and different maintenance strategies are used to estimate a variety of condition maintenance factors.An example of a subsea tree system is given to verify the effectiveness of the proposed method.