Adaptive Pinning Synchronization of Complex Networks with Negative Weights and Its Application in Traffic Road Network

  • Dan Wang
  • Wei-Wei Che
  • Hao Yu
  • Jia-Yang Li
Regular Paper Control Theory and Applications


As local traffic congestion and uncertainty factors existing on roads may lead to cascading failures or even large area traffic network congestion, a pinning control method is proposed to divert the traffic and then restore the smooth flow of traffic. To eliminate the impacts of uncertainties and negative weights for the traffic network performance, the adaptive pinning control and coupling adjustment strategies are designed to estimate controller parameters and adjust coupling strength to compensate for the impacts on the pinned nodes and unpinned nodes. Based on Lyapunov stability theory, adaptive pinning controllers and network adjusters are developed to guarantee the achievement of network synchronization even in the presence of the uncertainties and negative weights. In addition, we investigate the effects of the type of nodes on pinning synchronization performance. Numerical simulations show that if the network’s degree and the single node energy index are considered, better synchronization performance can be obtained by comparing with the pervious pinning schemes.


Adaptive pinning control complex traffic road network negative weights synchronization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. L. Wei, J. B. Qiu, and H. R. Karimi, “Fuzzy-affinemodel- based memory filter design of nonlinear systems with time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. PP, no. 99, pp. 1, 2017. [click]CrossRefGoogle Scholar
  2. [2]
    Y. L. Wei, J. B. Qiu, and H. R. Karimi, “Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults,” IEEE Transactions on Circuits and Systems–I: Regular Papers, vol. 64, no. 1, pp. 170–181, Junuary 2017.CrossRefGoogle Scholar
  3. [3]
    X. Z. Jin, Y. G. He, and Y. G. He, “Finite-time robust faulttolerant control against actuator faults and saturations,” IET Control Theory & Applications, vol. 11, no. 4, pp. 550–556, February 2017.MathSciNetCrossRefGoogle Scholar
  4. [4]
    X. Z. Jin, J. H. Qin, Y. Shi, and W. X. Zheng, “Auxiliary fault tolerant control with actuator amplitude saturation and limited rate,” IEEE Transactions on Systems, Man and Cybernetics: Systems, DOI: 10.1109/TSMC.2017.2752961, 2017.Google Scholar
  5. [5]
    J. Qin, W. Fu, W. X. Zheng, and H. Gao, “On the bipartite consensus for generic linear multiagent systems with input saturation,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1948–1958, August 2017.CrossRefGoogle Scholar
  6. [6]
    X. Z. Jin, Z. Zhao, and Y. G. He, “Insensitive leaderfollowing consensus for a class of uncertain multi-agent systems against actuator faults,” Neurocomputing, vol. 272, pp. 189–196, Junuary 2018.CrossRefGoogle Scholar
  7. [7]
    X. Z. Jin, S. F. Wang, G. H. Yang, and D. Ye, “Robust adaptive hierarchical insensitive tracking control of a class of leader-follower agents,” Information Sciences, vol. 406-407, pp. 234–247, May 2017.CrossRefGoogle Scholar
  8. [8]
    D. B. Tong, L. P. Zhang, W. N. Zhou, J. Zhou, and Y. H. Xu, “Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 706–712, June 2016. [click]CrossRefGoogle Scholar
  9. [9]
    M. Q. Liu, H. Y. Chen, S. L. Zhang, and W. H. Sheng, “H synchronization of two different discrete-time chaotic systems via a unified model,” International Journal of Control, Automation and Systems, vol. 13, no. 1, pp. 1393–1403, February 2015.Google Scholar
  10. [10]
    T. Chen, X. Liu, and W. Lu, “Pinning complex networks by a single controller,” IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 54, no. 6, pp. 1317–1326, June 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    X. Z. Jin and G. H. Yang, “Adaptive finite-time synchronization of a class of pinned and adjustable complex networks,” Nonlinear Dynamics, vol. 85, no. 3, pp. 1393–1403, August 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    J. Qin, Q. Ma, H. Gao, Y. Shi, and Y. Kang, “On group synchronization for interacting clusters of heterogeneous systems,” IEEE Transactions on Cybernetics, vol. 47, no. 12, pp. 4122–4133, December 2017.CrossRefGoogle Scholar
  13. [13]
    L. Dong, J. H. Wang, S. S. Gu, Y. B. Shi, and F. M. Zhao, “Adaptive synchronization of leader-follower networked systems against communication attenuation and actuators faults,” International Journal of Control, Automation, and Systems, vol. 14, no. 6, pp. 1484–1492, December 2016. [click]CrossRefGoogle Scholar
  14. [14]
    Z. K. Li, W. Ren, X. D. Liu, and M. Y. Fu, “Consensus of multi-agent systems with general linear and lipschitz nonlinear dynamics using distributed adaptive protocols,” IEEE Transactions on Automatic Control, vol. 58, no. 7, pp. 1786–1791, May 2011. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    X. Z. Jin, G. H. Yang, and W. W. Che, “Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 9, pp. 1345–1355, September 2012. [click]CrossRefGoogle Scholar
  16. [16]
    X. W. Liu and T. P. Chen, “Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control,” IEEE Transactions on Neural Networks & Learning Systems, vol. 26, no. 1, pp. 113–126, January 2015. [click]MathSciNetCrossRefGoogle Scholar
  17. [17]
    X. W. Liu and T. P. Chen, “Synchronization of complex networks via aperiodically intermittent pinning control,” IEEE Transactions on Automatic Control, vol. 60, no. 12, pp. 3316–3321, December 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    W. Guo, F. Austin, S. Chen, and W. Sun, “Pinning synchronization of the complex networks with non-delayed and delayed coupling,” Physics Letters A, vol. 373, no. 17, pp. 1565–1572, April 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    L. O. Chua, M. Itoh, L. Kocarev, and K. Eckert, “Chaos synchronization in Chua’s circuit,” Journal of Circuits, Systems and Computers, vol. 3, no. 1, pp. 93–108, 1993.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    I. Leyva, I. Sendina-Nadal, J. A. Alemendral, and M. A. F. Sanjuan, “Sparse repulsive coupling enhances synchronization in complex networks,” Physical Review E, vol. 74, no. 5, p. 056112, November 2006. [click]CrossRefGoogle Scholar
  21. [21]
    X. L. An, L. Zhang, and J. G. Zhang, “Research on urban public traffic network with multi-weights based on single bus transfer junction,” Physica A: Statistical Mechanics and its Applications, vol. 436, pp. 748–755, October 2015.MathSciNetCrossRefGoogle Scholar
  22. [22]
    L. Zhao, M. Deng, J. Q. Wang, and D. L. Peng, “Structural property analysis of urban street networks based on complex network theory,” Geography and Geo-Information Science, vol. 26, no. 5, pp. 11–15, May 2010.Google Scholar
  23. [23]
    P. Y. Ye, “Complex network characteristics of urban road network topology,” Journal of Transportation Engineering & Information (in chinese), vol. 1, pp. 12–19, Junuary 2012.Google Scholar
  24. [24]
    Y. Zhao, W. Du, and S. Chen, “Application of complex network theory to urban transportation network analysis,” Urban Transport of China (in chinese), vol. 7, no. 1, pp. 65–70, Junuary 2009.Google Scholar
  25. [25]
    Y. L. Wei, J. B. Qiu, H. K. Lam, and L. G. Wu, “Approaches to T-S fuzzy-affine-model-based reliable output feedback control for nonlinear ito stochastic systems,” IEEE Transactions on Fuzzy Systems, vol. 99, pp. 1-1, Junuary 2016.Google Scholar
  26. [26]
    Q. Jiang, J. Xiao, G. Zheng, Y. Zhang, and M. L. Wang, “A pinning scheme in complex networks based on energy index,” Control and Decision (in chinese), vol. 27, no. 1, pp. 22–27, Junuary 2012.MathSciNetzbMATHGoogle Scholar
  27. [27]
    M. J. Lighthill and G. B. Whitham, “On kinematic waves: I. flow movement in long rivers. II. a theory of traffic flow on long crowded roads,” Pharmacology & Therapeutics, vol. 53, no. 3, pp. 275–354, Junuary 1955.zbMATHGoogle Scholar
  28. [28]
    R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, Junuary 2007. [click]CrossRefzbMATHGoogle Scholar
  29. [29]
    L. F. Wang, H. Chen, and Y. Li, “Transition characteristic analysis of traffic evolution process for urban traffic network,” The Scientific World Journal, vol. 2014, 603274, 2014. [click]Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Manufacturing Industrial Integrated AutomationShenyang UniversityShenyang, LiaoningChina
  2. 2.College of Economics and ManagementShandong University of Science and TechnologyQingdao, ShandongChina
  3. 3.College of Information EngineeringShenyang UniversityShenyang, LiaoningChina

Personalised recommendations