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ABSTRACT: In this paper, the partial synchronization problem of stochastic dynamical networks (SDNs) is investigated. Unlike the existing models, the SDN considered in this paper suffers from a class of communication constraint-only part of nodes' states can be transmitted. Thus, less nodes' states can be used to synchronize the SDN, which makes the analysis of the synchronization problem much harder. A set of channel matrices are introduced to reflect such kind of constraint. Furthermore, due to unpredictable environmental changes, the channel matrices can switch among some communication modes. The switching considered here is governed by a Markov process. To overcome the difficulty, a regrouping method is employed to derive our main results. The obtained conditions guarantee that partial synchronization can be achieved for SDNs under switching communication constraint. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results and how the communication constraint influences synchronization result.
Chaos (Woodbury, N.Y.) 06/2012; 22(2):023108. · 1.80 Impact Factor
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ABSTRACT: We show that time-delayed feedback methods, which have successfully been used to control unstable steady states or periodic
orbits, provide a tool to control Hopf bifurcation for a small-world network model with nonlinear interactions and time delays.
We choose the interaction strength parameter as a bifurcation parameter. Without control, bifurcation will occur early; meanwhile,
the model can maintain a stationary total influenced volume only in a certain domain of the interaction strength parameter.
However, outside of this domain the model still possesses a stable total influenced volume that can be guaranteed by delayed
feedback perturbation, and the onset of the Hopf bifurcation is postponed. The feedback perturbation vanishes if the stabilization
is successful and thus the domain of stability can be extended under only small control force. We present an analytical investigation
of the feedback scheme using characteristic equation and discuss effects of both a low-pass filter included in the control
loop and nonzero latency times associated with generation and injection of the feedback signal.
Nonlinear Dynamics 04/2012; 58(1):319-344. · 1.25 Impact Factor
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ABSTRACT: This work considers the filtering problem for uncertain stochastic systems subject to sensor nonlinearities. It may be seen from simulation results in this work that the traditional filtering method based on linear measurement may not provide a reliable solution to this problem due to the existence of the nonlinear characteristic of sensors. In the system under consideration, there exist time-varying parameter uncertainties, and state and external-disturbance-dependent noise. Robust filters are constructed for both continuous and discrete stochastic systems, such that the resultant filtering error systems are robustly stochastically stable with a prescribed H ∞-disturbance attenuation performance. Finally, some simulation results with deterministic or stochastic disturbance signals are given to illustrate the proposed method.
International Journal of Systems Science. 05/2011; 42(5):737-749.
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ABSTRACT: This brief investigates globally exponential synchronization for linearly coupled neural networks (NNs) with time-varying delay and impulsive disturbances. Since the impulsive effects discussed in this brief are regarded as disturbances, the impulses should not happen too frequently. The concept of average impulsive interval is used to formalize this phenomenon. By referring to an impulsive delay differential inequality, we investigate the globally exponential synchronization of linearly coupled NNs with impulsive disturbances. The derived sufficient condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for large-scale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result.
IEEE Transactions on Neural Networks 02/2011; 22(2):329-36. · 2.95 Impact Factor
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IEEE Transactions on Signal Processing. 01/2011; 59:3048-3057.
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Int. J. Systems Science. 01/2011; 42:737-749.
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IEEE Transactions on Signal Processing. 01/2010; 58:2534-2543.
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IEEE T. Fuzzy Systems. 01/2010; 18:712-725.
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IEEE Transactions on Signal Processing. 01/2010; 58:6410-6416.
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IEEE T. Fuzzy Systems. 01/2010; 18:971-978.
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ABSTRACT: This paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks. Two types of impulses are considered: synchronizing impulses and desynchronizing impulses. In previous literature, all of the results are devoted to investigating these two kinds of impulses separately. Thus a natural question arises: Is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses? In this paper, a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named “average impulsive interval”. The derived criterion is theoretically and numerically proved to be less conservative than existing results. Numerical examples including scale-free and small-world structures are given to show that our results are applicable to large-scale networks.
Automatica. 01/2010;
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ABSTRACT: We study the consensus problem in directed static networks with arbitrary finite communication delays and consider both linear and nonlinear coupling. For the considered networked system, only locally delayed information is available for each node and also the information flow is directed. We find that consensus can be realized whatever the communications delays are. In fact, we do not even need to know the explicit values of the communication delays. One well-informed leader is proved to be enough for the regulation of all nodes' final states, even when the external signal is very weak. Numerical simulations for opinion formation in small-world and scale-free networks are given to demonstrate the potentials of our analytic results.
Physical Review E 12/2009; 80(6 Pt 2):066121. · 2.26 Impact Factor
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ABSTRACT: This article deals with the problem of computing an approximation system for a continuous-time switched stochastic system, such that the ∞ gain of the error system is less than a prescribed scalar. By using the average dwell-time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed, which guarantees the error system to be mean-square exponentially stable with a weighted ∞ performance. Then, the model reduction is solved by using the projection approach, which casts the model reduction into a sequential minimisation problem subjected to linear matrix inequality constraints by employing the cone complementary linearisation algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.
International Journal of Systems Science. 12/2009; 40(12):1241-1251.
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ABSTRACT: The globally exponential synchronization problem for general dynamical networks is considered in this paper. One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks.
IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics: a publication of the IEEE Systems, Man, and Cybernetics Society 10/2009; 40(2):350-61. · 3.01 Impact Factor
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ABSTRACT: Pinning stabilization problem of linearly coupled stochastic neural networks (LCSNNs) is studied in this paper. A minimum number of controllers are used to force the LCSNNs to the desired equilibrium point by fully utilizing the structure of the network. In order to pinning control the LCSNNs to a certain desired state, only one controller is required for strongly connected network topology, and m controllers, which will be shown to be the minimum number, are needed for LCSNNs with m -reducible coupling matrix. The isolate node of the LCSNNs can be stable, periodic, or even chaotic. The coupling Laplacian matrix of the LCSNNs can be symmetric irreducible, asymmetric irreducible, or m-reducible, which means that the network topology can be strongly connected, weakly connected, or even unconnected. There is no constraint on the network topology. Some criteria are derived to judge whether the LCSNNs can be controlled in mean square by using designed controllers. The given criteria are expressed in terms of strict linear matrix inequalities, which can be easily checked by resorting to recently developed algorithm. Moreover, numerical examples including small-world and scale-free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems.
IEEE Transactions on Neural Networks 09/2009; · 2.95 Impact Factor
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Int. J. Systems Science. 01/2009; 40:1241-1251.
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Automatica. 01/2009; 45:684-691.
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Complex Sciences, First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009. Revised Papers, Part 2; 01/2009
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Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, combined withe the 28th Chinese Control Conference, December 16-18, 2009, Shanghai, China; 01/2009
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ABSTRACT: This paper is concerned with the stabilization problem for a networked control system with Markovian characterization. We consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a Markov chain. The resulting closed-loop system is modeled as a Markovian jump linear system with two jumping parameters, and a necessary and sufficient condition on the existence of stabilizing controllers is established. An iterative linear matrix inequality (LMI) approach is employed to calculate a mode-dependent solution. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.
Automatica. 01/2009;
