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Synchronization of Nonlinear Dynamical Networks with Heterogeneous Impulses

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Handbook of Real-Time Computing

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Abstract

In this chapter, the synchronization problem is investigated for a class of nonlinear delayed dynamical networks with heterogeneous impulsive effects. The intrinsic properties of the heterogeneous impulses are that the impulsive strengths are heterogenous in both time and space domains, i.e., the impulsive effects in each node are not only nonidentical from each other, but also time-varying at different impulsive instants. The purpose of the addressed problem is to derive synchronization criteria such that, the nonlinear delayed dynamical networks with heterogeneous impulses can be synchronized to a desired state. By means of a time-dependent Lyapunov function and the comparison principle, several sufficient conditions are established under which the nonlinear dynamical networks with heterogeneous impulsive effects are exponentially synchronized to a desired state. An example is given to show the effectiveness of the proposed synchronization criterion.

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References

  • S. Boyd, L.E. Ghaoui, V. Balakrishnan, Linear matrix inequalities in system and control theory (SIAM, Philadelphia, 1994)

    Book  MATH  Google Scholar 

  • J. Cao, L. Li, Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw. 22, 335–342 (2009)

    Article  MATH  Google Scholar 

  • J. Cao, D.W.C. Ho, Y. Yang, Projective synchronization of a class of delayed chaotic systems via impulsive control. Phys. Lett. A 373, 3128–3133 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • T.P. Chen, Volatility modelling with heterogeneous impulse response function: introducing non-parametric jumps into the Fiegarch model. http://ssrn.com/abstract=1342785

  • W. Chen, D. Wei, W. Zheng, Delayed impulsive control of Takagi-Sugeno fuzzy delay systems. IEEE Trans. Fuzzy Syst 21, 516–526 (2013)

    Article  Google Scholar 

  • Y. Chen, W. Yu, F. Li, S. Feng, Synchronization of complex networks with impulsive control and disconnected topology. IEEE Trans. Circuits Syst. II Exp. Briefs 60, 292–296 (2013)

    Article  Google Scholar 

  • Z. Guan, Z. Liu, G. Feng, Y. Wang, Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans. Circuits Syst. I Regul. Pap. 57, 2182–2195 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • W. He, F. Qian, Q. Han, J. Cao, Lag quasi-synchronization of coupled delayed systems with parameter mismatch. IEEE Trans. Circuits Syst. I Regul. Pap. 58, 1345–1357 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • C. Hu, H. Jiang, Z. Teng, Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms. IEEE Trans. Neural Netw. 21, 67–81 (2010)

    Article  Google Scholar 

  • C. Li, G. Feng, T. Huang, On hybrid impulsive and switching neural networks. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38, 1549–1560 (2008)

    Article  Google Scholar 

  • Z. Li, Z. Duan, G. Chen, L. Huang, Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans. Circuits Syst. I Regul. Pap. 57, 213–224 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • B. Liu, X. Liu, G. Chen, H. Wang, Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuits Syst. I Regul. Pap. 52, 1431–1441 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Liu, Z. Wang, J. Liang, X. Liu, Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38, 1314–1325 (2008)

    Article  Google Scholar 

  • Y. Liu, Z. Wang, J. Liang, X. Liu, Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays. IEEE Trans. Cybern. 43, 102–114 (2013)

    Article  Google Scholar 

  • C. Lorand, P.H. Bauer, On synchronization errors in networked feedback systems. IEEE Trans. Circuits Syst. I Regul. Pap. 53, 2306–2317 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Lu, D.W.C. Ho, J. Cao, A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7), 1215–1221 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Lu, D.W.C. Ho, J. Cao, J. Kurths, Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans. Neural Netw. 22(2), 169–175 (2011)

    Article  Google Scholar 

  • J. Lu, Z. Wang, J. Cao, D. Ho, J. Kurths, Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int. J. Bifurcation Chaos 52, 1250176 (2012a)

    Article  MATH  Google Scholar 

  • J. Lu, J. Kurths, J. Cao, N. Mahdavi, C. Huang, Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst. 23, 285–292 (2012b)

    Article  Google Scholar 

  • E. Nuño, R. Ortega, L. Basañez, D. Hill, Synchronization of networks of nonidentical euler-lagrange systems with uncertain parameters and communication delays. IEEE Trans. Autom. Control 56, 935–943 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • L. Pan, J. Cao, Exponential synchronization for impulsive dynamical networks. Discret. Dyn. Nat. Soc. 2012, 232794 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • R. Saber, R. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49, 1520–1533 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Q. Song, J. Cao, Impulsive effects on stability of fuzzy cohencgrossberg neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 37, 733–741 (2007)

    Article  Google Scholar 

  • Y. Tang, W.K. Wong, Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Trans. Neural Netw. Learn. Syst. 24, 435–447 (2013)

    Article  Google Scholar 

  • Y. Tang, H. Gao, W. Zou, J. Kurths, Distributed synchronization in networks of agent systems with nonlinearities and random switchings. IEEE Trans. Cybern. 43, 358–370 (2013)

    Article  Google Scholar 

  • Z. Wang, Y. Wang, Y. Liu, Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans. Neural Netw. 21, 11–25 (2010)

    Article  Google Scholar 

  • Z. Wang, Z. Duan, J. Cao, Impulsive synchronization of coupled dynamical networks with nonidentical duffing oscillators and coupling delays. Chaos 22, 013140 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • W.K. Wong, W. Zhang, Y. Tang, X. Wu, Stochastic synchronization of complex networks with mixed impulses. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 2657–2667 (2013)

    Article  MathSciNet  Google Scholar 

  • Z. Wu, P. Shi, H. Su, J. Chu, Sampled-data synchronization of chaotic lure systems with time delays. IEEE Trans. Neural Netw. Learn. Syst. 38, 410–421 (2013)

    Google Scholar 

  • H. Xu, K.L. Teo, X. Liu, Robust stability analysis of guaranteed cost control for impulsive switched systems. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38, 1419–1422 (2008)

    Article  Google Scholar 

  • Z. Yang, D. Xu, Stability analysis and design of impulsive control systems with time delay. IEEE Trans. Autom. Control 52, 1448–1454 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Yang, J. Cao, Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects. Nonlinear Anal. Real World Appl. 11, 1650–1659 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • X. Yang, J. Cao, J. Lu, Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Trans. Circuits Syst. I Regul. Pap. 59, 371–384 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • X. Yang, J. Cao, J. Lu, Synchronization of randomly coupled neural networks with Markovian jumping and time-delay. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 363–376 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • W. Yu, G. Chen, W. Ren, J. Kurths, W. Zheng, Distributed higher order consensus protocols in multiagent dynamical systems. IEEE Trans. Circuits Syst. I Regul. Pap. 58, 1924–1932 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Zhang, Q. Han, Network-based synchronization of delayed neural networks. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 676–689 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • G. Zhang, Z. Liu, Z. Ma, Synchronization of complex dynamical networks via impulsive control. Chaos 17, 043126 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • H. Zhang, T. Ma, G. Huang, Z. Wang, Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans. Syst. Man Cybern. Part B Cybern. 40, 831–844 (2010)

    Article  Google Scholar 

  • W. Zhang, Y. Tang, J. Fang, X. Wu, Stability of delayed neural networks with time-varying impulses. Neural Netw. 36, 59–64 (2012)

    Article  MATH  Google Scholar 

  • W. Zhang, Y. Tang, Q. Miao, W. Du, Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans. Neural Netw. Learn. Syst. 24, 1316–1326 (2013)

    Article  Google Scholar 

  • J. Zhao, D.J. Hill, T. Liu, Stability of dynamical networks with non-identical nodes: a multiple v-lyapunov function method. Automatica 47, 2615–2625 (2011a)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Zhao, D.J. Hill, T. Liu, Synchronization of dynamical networks with nonidentical nodes: criteria and control. IEEE Trans. Circuits Syst. I Regul. Pap. 58, 584–594 (2011b)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Zhou, T. Chen, Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuits Syst. I Regul. Pap. 53, 733–744 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Z. Zhu, H. Hu, Robust synchronization by time-varying impulsive control. IEEE Trans. Circuits Syst. II Exp. Briefs 57, 735–739 (2010)

    Article  Google Scholar 

  • J. Zhu, J. Lu, X. Yu, Flocking of multi-agent non-holonomic systems with proximity graphs. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 199–210 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Yangzhou University, Jiangsu, China

    Wenbing Zhang

  2. The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai, China

    Yang Tang

  3. School of Continuing Education, Shanghai Jiao Tong University, Shanghai, China

    Qingying Miao

Authors
  1. Wenbing Zhang
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  2. Yang Tang
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  3. Qingying Miao
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Corresponding author

Correspondence to Wenbing Zhang .

Editor information

Editors and Affiliations

  1. School of Computer Science, Queensland University of Technology, Brisbane, QLD, Australia

    Yu-Chu Tian

  2. School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW, Australia

    David Charles Levy

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Zhang, W., Tang, Y., Miao, Q. (2022). Synchronization of Nonlinear Dynamical Networks with Heterogeneous Impulses. In: Tian, YC., Levy, D.C. (eds) Handbook of Real-Time Computing. Springer, Singapore. https://doi.org/10.1007/978-981-287-251-7_22

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