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 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 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 problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of t...The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabasi-Albert model and various star-shaped networks are performed for verification and illustration.展开更多
This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small ...This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.展开更多
The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the...The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.展开更多
In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a ...In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis.展开更多
We review the research on complex dynamical networks(CDNs)with impulsive effects.We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects,where im...We review the research on complex dynamical networks(CDNs)with impulsive effects.We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects,where impulsive effects are considered from two aspects,i.e.,impulsive control and impulsive perturbation.Five aspects of CDNs with impulsive effects are surveyed,including synchronizing impulses,desynchronizing impulses,adaptive-impulsive synchronization,pinning impulsive synchronization,and CDNs with stochastic and impulsive effects.Finally,conclusions and some future research directions are briefly addressed.展开更多
This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simpl...This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.展开更多
Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic s...Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities （LMIs）, which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogenous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.展开更多
Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are ...Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems.The numerical simulations,whose theoretical results are applied to robust synchronization of complex networks,demonstrate the effectiveness and feasibility of the proposed technique.展开更多
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.
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Project supported by the National Natural Science Foundation of China (Grant No 60674093)the Foundation for Key Program of Ministry of Education,China (Grant No 107110)
文摘The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabasi-Albert model and various star-shaped networks are performed for verification and illustration.
基金Project supported by the Aviation Science Funds (Grant No 20080751019)
文摘This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.
基金supported by National Natural Science Foundation of China(No.61273008)Science Research Project of Liaoning Provicial Education Department(No.L2012208)Science Foundation of Ministry of Housing and Urban-Rural Development(No.2013-K5-2)
文摘The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.
基金the National Natural Science Foundation of China (No.60774088, 60574036)the Program for New Century ExcellentTalents in University of China (NCET)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20050055013)the Science & Technology Research Key Project of Education Ministry of China (No.107024)
文摘In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis.
基金Project supported by the National Natural Science Foundation of China(No.61673247)the Research Fund for Excellent Young Scholars of Shandong Province,China(No.JQ201719)。
文摘We review the research on complex dynamical networks(CDNs)with impulsive effects.We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects,where impulsive effects are considered from two aspects,i.e.,impulsive control and impulsive perturbation.Five aspects of CDNs with impulsive effects are surveyed,including synchronizing impulses,desynchronizing impulses,adaptive-impulsive synchronization,pinning impulsive synchronization,and CDNs with stochastic and impulsive effects.Finally,conclusions and some future research directions are briefly addressed.
文摘This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.
基金the National Natural Science Fundation of China (Grant Nos. 60774088 and 60574036)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050055013)and the Program for New Century Excellent Talents of China (NCET)
文摘Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities （LMIs）, which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogenous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.
基金supported by Project of Shandong Province Higher Educational Science and Technology Program(J13LI02)Research Fund Project of Heze University under Grant:XY10KZ01
文摘Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems.The numerical simulations,whose theoretical results are applied to robust synchronization of complex networks,demonstrate the effectiveness and feasibility of the proposed technique.
