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Weighted Small World Complex Networks: Smart Sliding Mode Control

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Emerging Intelligent Computing Technology and Applications. With Aspects of Artificial Intelligence (ICIC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5755))

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Abstract

In this paper, we establish a novel weighted small world complex network which is generated by assigning special weight to rewired links according to concrete scenarios. The smart sliding mode control for weighted small world complex networks is developed based on the ergordicity characteristic of chaos dynamical systems. The most distinctive of this scheme is without involvement of linearization and other ideal assumptions, which forces system state of the modified small-world complex network to approach to the desired manifolds and eventually realize the asymptotical synchronization behavior of weighted small world complex networks.

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References

  1. Watts, D.J., Strogatz, S.H.: Collective Dynamics of Small-world Networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  2. Strogatz, S.H.: Exploring Complex Networks. Nature 410, 268–276 (2001)

    Article  Google Scholar 

  3. Barabasi, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  4. Barabasi, A.L., Albert, R., Jeong, H.: Mean-field Theory for Scale-free Random Networks. Physcia A 272, 173–187 (1999)

    Article  Google Scholar 

  5. Holmgren, A.J.: Using Graph Models to Analyze the Vulnerability of Electric Power Networks. Risk Analysis 26(4), 955–969 (2006)

    Article  Google Scholar 

  6. Wang, X.F., Chen, G.: Complex Networks: Small-world, Scale-free, and Beyond. IEEE Circuits Syst. Mag. 3(1), 6–20 (2003)

    Article  Google Scholar 

  7. Abdallah, C.T., Tanner, H.R.: Complex Networked Control Systems: Introduction to the Special Section. IEEE Control Systems Magazine, 30–32 (2007)

    Google Scholar 

  8. Wang, X.F., Chen, G.: Pinning Control of Scale-free Dynamical Networks. Physica A 310, 521–531 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen, T., Liu, X., Lu, W.: Pinning Complex Network by a Single Controller. IEEE Trans Circuits and Systems-I: Regular Papers 54(6), 1317–1326 (2006)

    Article  MathSciNet  Google Scholar 

  10. Wang, X.F., Chen, G.: Synchronization in Scale-free Dynamical Networks: Robustness and Fragility. IEEE Trans Circuits and Systems-I: Fundamental Theory and Applications 49(1), 54–62 (2002)

    Article  MathSciNet  Google Scholar 

  11. Lü, J., Yu, X., Chen, G., et al.: Characterizing the Synchronizability of Small-world Dynamical Networks. IEEE Trans Circuits and Systems-I: Regular Papers 51(4), 787–796

    Google Scholar 

  12. Li, C., Chen, G.: Synchronization in General Complex Dynamical Networks with Coupling Delays. Physica A 343, 263–278 (2004)

    Article  MathSciNet  Google Scholar 

  13. Lü, J., Chen, G.: A Time-varying Complex Dynamical Network Model and Its Controlled Synchronization Criteria. IEEE Trans Automatic Control 50(6), 841–846 (2005)

    Article  Google Scholar 

  14. Liu, B., Liu, X., Chen, G., et al.: Robust Impulsive Synchronization of Uncertain Dynamical Networks. IEEE Trans Circuits and Systems-I: Regular Papers 52(7), 1431–1441 (2005)

    Article  MathSciNet  Google Scholar 

  15. Yang, M., Wang, Y., Wang, H.O., et al.: Delay Independent Synchronization of Complex Network via Hybrid Control. In: Proceedings of 2008 American Control Conference, Seattle, Washington, USA, pp. 2206–2271 (2008)

    Google Scholar 

  16. Chen, M.: Chaos Synchronization in Complex Network. IEEE Trans Circuits and Systems-I: Regular Papers 55(5), 1335–1346 (2008)

    Article  MathSciNet  Google Scholar 

  17. Pecora, L.M., Carroll, T.L.: Master Stability Functions for Synchronized Coupled Systems. Physical Review Letters 80, 2109–2112 (1998)

    Article  Google Scholar 

  18. Chavez, M., Hwang, D., Amann, A., et al.: Synchronizing is Enhanced in Weighted Complex Networks. Physical Review Letters 94(21), 8701 (2005)

    Article  Google Scholar 

  19. Wu, C.W.: Synchronization and Convergence of Linear Dynamics in Random Directed Networks. IEEE Trans Automatic Control 51(7), 1207–1210 (2006)

    Article  Google Scholar 

  20. Jalili, M., Ajdari, R.A., Hasler, M.: Enhancing Synchronizability of Dynamical Networks Using the Connection Graph Stability Method. Int. J. Ciurcuit Theory Appl. 35, 611–622 (2007)

    Article  MATH  Google Scholar 

  21. Jalili, M., Ajdari, R.A., Hasler, M.: Enhancing Synchronizability of Weighted Dynamical Networks Using Betweenness Centrality. Physical Review E 78, 16105 (2008)

    Article  Google Scholar 

  22. Utkin, V.I.: Sliding Modes in Control Optimization. Springer, Berlin (1992)

    MATH  Google Scholar 

  23. Yu, X.: Controlling Lorenz Chaos. International Journal of Systems Science 27(4), 355–359 (1996)

    Article  MATH  Google Scholar 

  24. Tian, Y.P., Yu, X.: Adaptive Control of Chaotic Dynamical Systems Using Invariant Manifold Approach. IEEE Trans Circuits and Systems-I: Fundamental Theory and Applications 47(10), 1537–1542 (2000)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, 225009, China

    Yuequan Yang

  2. School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC, 3001, Australia

    Xinghuo Yu

Authors
  1. Yuequan Yang
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  2. Xinghuo Yu
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Editor information

Editors and Affiliations

  1. Institute of Intelligent Machines, Chinese Academy of Sciences, China

    De-Shuang Huang

  2. Graduate School of Electrical Engineering, University of Ulsan, Korea, San 29, Mugeo-Dong, Nam-Ku, 680 - 749, Ulsan, Korea

    Kang-Hyun Jo

  3. School of Electrical Engineering, University of Ulsan, Ulsan, South Korea

    Hong-Hee Lee

  4. School of Electrical Engineering, University of Ulsan, South Korea

    Hee-Jun Kang

  5. e.B.I.S. s.r.l. (electronic Business in Security), Spin-Off of Polytechnic of Bari, Str. Prov. per Casamassima Km., 3, 70010, Valenzano, (BA), Italy

    Vitoantonio Bevilacqua

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© 2009 Springer-Verlag Berlin Heidelberg

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Yang, Y., Yu, X. (2009). Weighted Small World Complex Networks: Smart Sliding Mode Control. In: Huang, DS., Jo, KH., Lee, HH., Kang, HJ., Bevilacqua, V. (eds) Emerging Intelligent Computing Technology and Applications. With Aspects of Artificial Intelligence. ICIC 2009. Lecture Notes in Computer Science(), vol 5755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04020-7_101

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  • DOI: https://doi.org/10.1007/978-3-642-04020-7_101

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04019-1

  • Online ISBN: 978-3-642-04020-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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