Pinning Complex Networks by a Single Controller

Chen, Tianping; Liu, Xiwei; Lu, Wenlian

doi:10.1109/tcsi.2007.895383

Cited by 963 publications

(569 citation statements)

References 22 publications

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“…[6][7][8][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] In particular, the study on controlling the dynamics of a network and guiding it to a desired state, such as, an equilibrium point or a periodic orbit of the network has become an interesting and important direction in this research field. 7,[18][19][20][22][23][24]26,27 It has been revealed that, in the process of controlling various networks, feedback control serves as a simple and effective approach for stabilization and synchronization. However, it is widely believed that it is impossible to add controllers to all nodes.…”

Section: Introductionmentioning

confidence: 99%

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Pinning control of fractional-order weighted complex networks

Tang

Wang

Fang

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

129

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In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3068350͔Recently, fractional-order differential systems have been widely investigated due to their potential applications in viscoelasticity, dielectric polarization, quantum evolution of complex systems, and many other fields. On the other hand, research of complex networks has triggered tremendous interest during the past decade. Most studies to date have concerned integer-order complex networks. In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The fractional-order complex networks generalize wellstudied integer-order complex networks. Some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated by utilizing the eigenvalue analysis and fractional-order stability theory. A surprising finding that the fractional-order networks can stabilize itself by reducing the fractional-order q without pinning any node is presented. The numerical algorithms for fractional-order networks are also presented. In the end, computer simulations in scale-free networks are given to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger coupling strength c, the more capacity that the pinning strategy can possess to accelerate the control rate of fractional-order networks.

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Section: Introductionmentioning

confidence: 99%

“…To reduce the control cost, some feedback injections may be added to a fraction of network nodes, which is known as pinning control. [17][18][19][20][22][23][24]26,27,33 In Ref. 17, pinning control of spatiotemporal chaos was discussed.…”

Section: Introductionmentioning

confidence: 99%

Pinning control of fractional-order weighted complex networks

Tang

Wang

Fang

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

129

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“…Besides, [9] showed the number of node which should be pinned in a complex network in order to reach synchronization. It can be seen that in [13][14][15][16][17] that pinning adaptive method is very effective for solving synchronization of complex networks. In [16], the authors investigated the synchronization of nonlinearly coupled networks through an innovative local adaptive approach.…”

Section: Introductionmentioning

confidence: 99%

On Synchronization of Pinning-Controlled Networks with Reducible and Asymmetric Coupling Matrix

Xuan¹,

Feng

Feng³

et al. 2011

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This paper investigates the synchronization of directed networks whose coupling matrices are reducible and asymmetrical by pinning-controlled schemes. A strong sufficient condition is obtained to guarantee that the synchronization of the kind of networks can be achieved. For the weakly connected network, a method is presented in detail to solve two challenging fundamental problems arising in pinning control of complex networks: 1) How many nodes should be pinned? 2) How large should the coupling strength be used in a fixed complex network to realize synchronization? Then, we show the answer to the question that why all the diagonal block matrices of Perron-Frobenius normal matrices should be pinned? Besides, we find out the relation between the Perron-Frobenius normal form of coupling matrix and the differences of two synchronization conditions for strongly connected networks and weakly connected ones with linear coupling configuration. Moreover, we propose adaptive feedback algorithms to make the coupling strength as small as possible. Finally, numerical simulations are given to verify our theoretical analysis.

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“…It is a phenomenon that has been widely investigated since it was discovered by Pecora and Carroll in 1990 [8]. Many synchronization patterns have been explored (for example, complete synchronization [9][10][11], cluster synchronization [12,13], phase synchronization [14], partial synchronization [15], projective synchronization [16,17]), and synchronization can be achieved by the use of pinning control [18,19], adaptive control [20][21][22], intermittent control [23], impulsive control [24,25], fuzzy control [26], hybrid control [27] or active control [28].…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of Two Complex Dynamical Networks of Random Disturbance with Both Mixed Coupled and Time-Varying Delay by Pinning Control

2015

Entropy

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In this paper, the exponentially synchronization in the mean square is investigated for two different stochastic complex networks with hybrid coupling and time-varying delay via pinning control. By utilizing the Lyapunov stability theory, stochastic analysis theory, as well as matrix analysis, the sufficient conditions are derived to guarantee the exponential synchronization for any initial values through a feedback scheme. The numerical simulation is provided to show the effectiveness of the theoretical results.

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Pinning Complex Networks by a Single Controller

Cited by 963 publications

References 22 publications

Pinning control of fractional-order weighted complex networks

Pinning control of fractional-order weighted complex networks

On Synchronization of Pinning-Controlled Networks with Reducible and Asymmetric Coupling Matrix

Exponential Synchronization of Two Complex Dynamical Networks of Random Disturbance with Both Mixed Coupled and Time-Varying Delay by Pinning Control

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