Criteria for global pinning-controllability of complex networks

Porfiri, Maurizio; Bernardo, Mario di

doi:10.1016/j.automatica.2008.05.006

Cited by 242 publications

(141 citation statements)

References 20 publications

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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: 98%

“…In [16], the authors investigated the synchronization of nonlinearly coupled networks through an innovative local adaptive approach. By using the technique of pinning only a limited subset of the whole network, [17] showed that the complex network with coupled identical oscillators could be driven onto some desired common reference trajectory. Nowadays, more and more attentions are being paid to the optimization problems of pinning schemes [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Introductionmentioning

confidence: 98%

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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“…It is worth pointing out that the parameter γ k affects the solvability of the equations (19) and (20). In the implementation, the value of γ k could be given a prior and adjusted to help enhance the solvability and feasibility of the developed estimation scheme.…”

Section: Imentioning

confidence: 99%

A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements

et al. 2016

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In this paper, the recursive state estimation problem is investigated for an array of discrete time-varying coupled stochastic complex networks with missing measurements. A set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements, where each sensor can have individual missing probability. The Taylor series expansion is employed to deal with the nonlinearities and the high-order terms of the linearization errors are estimated. The purpose of the addressed state estimation problem is to design a time-varying state estimator such that, in the presence of the missing measurements and the random disturbances, an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given. By using the Riccatilike difference equations approach, the estimator parameter is characterized by the solutions to two Riccati-like difference equations. It is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme.

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“…And later on, Yu et al [36] concerned with pinning performance of complex dynamical network. Other research works about pinning control of complex networks can be seen in [8,12,17,22,23,24,26,30,31,32,33,34,35,40,41] and many references cited therein.…”

Section: Introductionmentioning

confidence: 99%

“…To reduce the number of controlled nodes, some feedback injections have been added to a fraction of network nodes, which is known as pinning control. As a result, some researchers have focused on the investigations different pinning control strategies for various complex dynamical networks [5,8,10,14,22,23,24,25,26,29,30,31,32,33,34,35,36,39]. For example, Wang and Chen [29] revealed that, it is much more effective to pin some most-highly connected nodes than to pin randomly selected nodes since the extremely inhomogeneous connectivity distribution of scale-free networks.…”

Section: Introductionmentioning

confidence: 99%