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,...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.展开更多
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 ...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.展开更多
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 spontaneous...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.展开更多
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 trans...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.展开更多
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 a...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.展开更多
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 stabil...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.展开更多
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 feedba...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.展开更多
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 approa...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.展开更多
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 fu...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.展开更多
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...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.展开更多
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, inequal...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.展开更多
A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical syn...A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical synchronization and all the closed-loop signals are bounded. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible and asymptotical synchronization can be achieved even when the graph of network is not connected. Finally, a simulation example shows the feasibility and effectiveness of the approach.展开更多
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 asy...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.展开更多
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 dri...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.展开更多
In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the ...In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the Lyapunov function method and mathematical analysis technique, a synchronization criterion with respect to the impulsive gains and intervals is analytically derived. From the criterion, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some constants are fixed, and vice versa. Finally, two numerical examples are provided to verify the effectiveness of the derived result.展开更多
This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling...This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling, two networks may synchronize if the coupling strength and the on-off rate are large enough. It is shown that, for undirected and strongly connected networks, the upper bound of time delays for synchronization is a decreasing function of the absolute value of the minimum eigenvalue of the adjacency matrix. The theoretical analysis confirms the numerical results and provides a better understanding of the influence of time delays and on-off coupling on the synchronization transition. The influence of random delays on the synchronization is also discussed.展开更多
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...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.展开更多
This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown co...This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.展开更多
The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned n...The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.展开更多
This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback con...This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.72071153 and 72231008)Laboratory of Science and Technology on Integrated Logistics Support Foundation (Grant No.6142003190102)the Natural Science Foundation of Shannxi Province (Grant No.2020JM486)。
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62373197 and 61873326)。
文摘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.
基金supported by the National Natural Science Foundation of China(62172170)the Science and Technology Project of the State Grid Corporation of China(5100-202199557A-0-5-ZN).
文摘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.
基金the National Natural Science Foundation of China (No.60874024, 60574013).
文摘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.
文摘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.
基金supported in part by the National Natural Science Foundation of China (Grant Nos.60874091 and 61104103)the Natural Science Fund for Colleges and Universities in Jiangsu Province,China (Grant No.10KJB120001)the Climbing Program of Nanjing University of Posts & Telecommunications,China (Grant Nos.NY210013 and NY210014)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.61004101)the Natural Science Foundation Program of Guangxi Province,China(Grant No.2015GXNSFBB139002)+1 种基金the Graduate Innovation Project of Guilin University of Electronic Technology,China(Grant No.GDYCSZ201472)the Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin University of Electronic Technology,China
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472091, 10502042 and 10332030) Graduate Starting Seed Fund of Northwestern Polytechnical University, China (Grant No Z200655)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No 10832006)the Key Projects of Educational Ministry of China (Grant No 107110)
文摘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.
基金supported in part by the Program for New Century Excellent Talents in University of China (Grant No. NCET-06-0510)the National Natural Science Foundation of China (Grant No. 60874091)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No.60974139)the Fundamental Research Funds for the Central Universities (Grant No.72103676)
文摘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.
基金supported by Ph.D.Programs Foundation of Ministry of Education of China(Nos.JY0300137002 and20130203110021)Research Funds for the Central Universities(No.JB142001-6)
文摘A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical synchronization and all the closed-loop signals are bounded. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible and asymptotical synchronization can be achieved even when the graph of network is not connected. Finally, a simulation example shows the feasibility and effectiveness of the approach.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60274099)the National High Technology Research and Development Program of China (Grant No. 2004AA412030)
文摘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.
基金Sponsored by the Cooperation Building Foundation Project of Beijing Education Committee (100070
文摘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.
基金Supported by the Tianyuan Special Funds of the NSFC under Grant No.11226242the Natural Science Foundation of Jiangxi Province of China under Grant Nos.20122BAB211006 and 20132BAB201016
文摘In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the Lyapunov function method and mathematical analysis technique, a synchronization criterion with respect to the impulsive gains and intervals is analytically derived. From the criterion, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some constants are fixed, and vice versa. Finally, two numerical examples are provided to verify the effectiveness of the derived result.
基金Supported by the National Natural Science Foundation of China under Grant No.61681240393the Fundamental Research Funds for the Central Universities under Grant No.2015XKMS076
文摘This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling, two networks may synchronize if the coupling strength and the on-off rate are large enough. It is shown that, for undirected and strongly connected networks, the upper bound of time delays for synchronization is a decreasing function of the absolute value of the minimum eigenvalue of the adjacency matrix. The theoretical analysis confirms the numerical results and provides a better understanding of the influence of time delays and on-off coupling on the synchronization transition. The influence of random delays on the synchronization is also discussed.
基金Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103223110003)The Ministry of Education Research in the Humanities and Social Sciences Planning Fund, China (Grant No. 12YJAZH120)
文摘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.
文摘This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.
基金the National Natural Science Foundation of China (No.60774088, 60504017)the Specialized Research Fund for theDoctoral Program of Higher Education of China (No.20050055013)the Program for New Century Excellent Talents of China (NCET)
文摘The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.
基金supported by Key Projectof Natural Science Foundation of China(61833005)the Natural Science Foundation of Hebei Province of China(A2018203288)。
文摘This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.
