Skip to main content
SpringerLink
Log in

Asymptotical Tracking Control of Complex Dynamical Network Based on Links State Observer

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper studies how to design a control scheme for a complex dynamical network (CDN) such that the state of nodes and links can track on any given reference signals respectively, under the view that the CDN is coupled by the nodes and links. Since the dynamic behavior of the links reflects the changes in network topology(NT), the weights of the links are regarded as state variables of the NT. In addition, since the state of the links is not always avaluable in practical engineering applications, in order to address this problem, this paper provides an asymptotical state observer that uses its observation values to estimate the links state. Based on this, this paper proposes a new control scheme which designs controllers in the nodes and links respectively, to realize the asymptotical tracking control of the nodes and links. In order to understand the NT tracking target, an illustrative example is that the star topology can be chosen as the NT tracking target of communication transmission network for the centralized management. Finally, the validity of the theoretical results is verified by a numerical experiment that applies the control scheme to a helicopter model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. T. Gao, Y. H. Wang, Y. Peng, L. L. Zhang, and Y. Y. Huang, “Tracking control for the nonlinear complex dynamical network assisted with outgoing links dynamics,” International Journal of Robust and Nonlinear Control, vol. 32, no. 16, pp. 8754–8766, July 2022.

    Article  MathSciNet  Google Scholar 

  2. X. X. Li, Y. H. Wang, and L. Z. Liu, “Model Following adaptive control for a class of complex dynamic networks based on the dynamics of links,” International Journal of Control, Automation, and Systems, vol. 20, no. 7, pp. 2202–2210, June 2022.

    Article  Google Scholar 

  3. P. T. Gao, Y. H. Wang, L. Z. Liu, L. L. Zhang, and X. Tang, “Asymptotical state synchronization for the controlled directed complex dynamic network via links dynamics,” Neurocomputing, vol. 448, pp. 60–66, August 2021.

    Article  Google Scholar 

  4. L. Z. Liu, Y. H. Wang, and Z. L. Gao, “Tracking control for the dynamic links of discrete-time complex dynamical network via state observer,” Applied Mathematics and Computation, vol. 369, 124857, March 2020.

    Article  MathSciNet  Google Scholar 

  5. Z. L. Gao, Y. H. Wang, Y. Peng, L. Z. Liu, and H. G. Chen, “Adaptive control of the structural balance for a Class of complex dynamical networks,” Journal of Systems Science and Complexity, vol. 33, no. 3, pp. 725–742, April 2020.

    Article  MathSciNet  Google Scholar 

  6. Z. L. Gao, Y. H. Wang, J. Xiong, L. L. Zhang, and W. L. Wang, “Robust state observer design for dynamic connection relationships in complex dynamical networks,” International Journal of Control, Automation, and Systems, vol. 17, no. 2, pp. 336–344, January 2019.

    Article  Google Scholar 

  7. Y. H. Wang, W. L. Wang, and L. L. Zhang, “State synchronization of controlled nodes via the dynamics of links for complex dynamical networks,” Neurocomputing, vol. 384, pp. 225–230, April 2020.

    Article  Google Scholar 

  8. Z. Wu, X. J. Xu, G. R. Chen, and X. C. Fu, “Generalized matrix projective synchronization of general colored networks with different-dimensional node dynamics,” Journal of the Franklin Institute, vol. 351, no. 9, pp. 4584–4595, September 2014.

    Article  MathSciNet  Google Scholar 

  9. X. F. Wang and G. R. Chen, “Synchronization in scale-free dynamical networks: Robustness and fragility,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 1, pp. 54–62, September 2002.

    Article  MathSciNet  Google Scholar 

  10. X. F. Wang and G. R. Chen, “Synchronization in small-world dynamical networks,” International Journal of Bifurcation and Chaos, vol. 12, no. 01, pp. 87–192, January 2002.

    Article  Google Scholar 

  11. J. Gómez-Gardenes, S. Gómez, A. Arenas, and Y. Moreno, “Explosive synchronization transitions in scale-free networks,” Physical Review Letters, vol. 106, no. 12, 128701, March 2011.

    Article  Google Scholar 

  12. M. Roy, A. Senapati, S. Poria, A. Mishra, and C. Hens, “Role of assortativity in predicting burst synchronization using echo state network,” Physical Review E, vol. 105, no. 6, 064205, June 2022.

    Article  MathSciNet  Google Scholar 

  13. P. DeLellis, M. Di Bernardo, T. E. Gorochowski, and G. Russo, “Synchronization and control of complex networks via contraction, adaptation and evolution,” IEEE Circuits and Systems Magazine, vol. 10, no. 3, pp. 64–82, August 2010.

    Article  Google Scholar 

  14. L. Chai, J. Liu, G. R. Chen, and X. Zhao, “Dynamics and synchronization of a complex-valued star network,” Science China Technological Sciences, vol. 64, no. 12, pp. 2729–2743, November 2021.

    Article  Google Scholar 

  15. S. Sabarathinam and A. Prasad, “Generalized synchronization in a conservative and nearly conservative systems of star network,” Chaos, vol. 28, no. 11, 113107, November 2018.

    Article  MathSciNet  Google Scholar 

  16. C. Meena, K. Murali, and S. Sinha, “Chimera states in star networks,” International Journal of Bifurcation and Chaos, vol. 26, no. 09, 1630023, May 2016.

    Article  MathSciNet  Google Scholar 

  17. P. Pagilla, N. Siraskar, and R. Dwivedula, “Decentralized control of web processing lines,” IEEE Transactions on Control Systems Technology, vol. 15, no. 1, pp. 106–117, January 2007.

    Article  Google Scholar 

  18. H. L. Hou, X. H. Nian, H. Y. Xiong, Z. Wang, and Z. Peng, “Robust decentralized coordinated control of a multimotor web-winding system,” IEEE Transactions on Control Systems Technology, vol. 24, no. 4, pp. 1495–1503, July 2016.

    Article  Google Scholar 

  19. C. Li and Z. Kang, “Synchronization control of complex network based on extended observer and sliding mode control,” IEEE Access, vol. 8, pp. 77336–77343, April 2020.

    Article  Google Scholar 

  20. G. Z. Wang, F. Zhao, X. Y. Chen, and J. L. Qiu, “Observer-based finite-time H∞ control of Itô-type stochastic nonlinear systems,” Asian Journal of Control, vol. 25, no. 3, pp. 1–10, October 2022.

    Google Scholar 

  21. G. P. Jiang, W. K. Tang, and G. R. Chen, “A state-observer-based approach for synchronization in complex dynamical networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 12, pp. 2739–2745, December 2006.

    Article  MathSciNet  Google Scholar 

  22. Y. H. Wang, Y. Q. Fan, Q. Y. Wang, and Y. Zhang, “Stabilization and synchronization of complex dynamical networks with different dynamics of nodes via decentralized controllers,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 8, pp. 1786–1795, August 2012.

    MathSciNet  Google Scholar 

  23. W. Wu and T. P. Chen, “Global synchronization criteria of linearly coupled neural network systems with time-varying coupling,” IEEE Transactions on Neural Networks, vol. 19, no. 2, pp. 319–332, February 2008.

    Article  Google Scholar 

  24. Z. Li and G. R. Chen, “Global synchronization and asymptotic stability of complex dynamical networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 1, pp. 28–33, January 2006.

    Article  Google Scholar 

  25. Z. S. Duan, J. Z. Wang, G. R. Chen, and L. Huang, “Stability analysis and decentralized control of a class of complex dynamical networks,” Automatica, vol. 44, no. 4, pp. 1028–1035, April 2008.

    Article  MathSciNet  Google Scholar 

  26. Z. K. Li, Z. S. Duan, G. R. Chen, and L. Huang, “Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 1, pp. 213–224, June 2010.

    MathSciNet  Google Scholar 

  27. Y. Shang, M. Y. Chen, and J. Kurths, “Generalized synchronization of complex networks,” Physical Review E, vol. 80, pp. 27201–27204, August 2009.

    Article  Google Scholar 

  28. C. Y. Wang and Y. H. Wang, “Stability analysis of discretized structure systems based on the complex network with dynamics of time-varying stiffness,” Mathematical Methods in the Applied Sciences, vol. 44, no. 17, pp. 13344–13356, July 2021.

    Article  MathSciNet  Google Scholar 

  29. F. Liao, J. Wang, and G. Yang, “Reliable robust flight tracking control: An LMI approach,” IEEE Transactions on Control Systems Technology, vol. 10, no. 1, pp. 76–89, January 2002.

    Article  Google Scholar 

  30. R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, New York, 2012.

    Book  Google Scholar 

  31. H. Neudecker, “A matrix trace inequality,” Journal of Mathematical Analysis and Applications, vol. 166, no. 1, pp. 302–303, May 1992.

    Article  MathSciNet  Google Scholar 

  32. M. Nishi, M. Ishitobi, and K. Nakasaki, “Nonlinear adaptive control system design and experiment for a 3-DOF model helicopter,” Artificial Life and Robotics. vol. 13, no. 1, pp. 50–53, December 2008.

    Article  Google Scholar 

  33. J. Yang and W. Hsu, “Adaptive backstepping control for electrically driven unmanned helicopter,” Control Engineering Practice, vol. 17, no. 8, pp. 903–913, August 2009.

    Article  Google Scholar 

  34. J. Vilchis, B. Brogliato, A. Dzul, and R. Lozano, “Nonlinear modelling and control of helicopters,” Automatica, vol. 39, no. 9, pp. 1583–1596, September 2003.

    Article  MathSciNet  Google Scholar 

  35. T. Wu, J. D. Cao, C. K. Ahn, L. L. Xiong, Y. Liu, and H.-K. Lam, “Anti-attack protocol-based synchronization control for fuzzy complex dynamic networks,” IEEE Transactions on Fuzzy Systems, vol. 32, no. 6, pp. 3433–3443, 2024.

    Article  Google Scholar 

  36. D. Y. Zhao, S. Y. Li, and Q. M. Zhu, “Adaptive synchronised tracking control for multiple robotic manipulators with uncertain kinematics and dynamics,” International Journal of Systems Science, vol. 47, no. 4, pp. 791–804, April 2016.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Guangzhou Railway Polytechnic, Guangzhou, 511300, China

    Juan-xia Zhao

  2. School of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Yin-he Wang

  3. School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou, 510006, China

    Pei-tao Gao

Authors
  1. Juan-xia Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yin-he Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pei-tao Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pei-tao Gao.

Ethics declarations

The authors declare no potential conflict of interests.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by the Scientific Research Startup Project of Guangdong Polytechnic Normal University (991701003), the National Natural Science Foundation of China (62273108).

Juan-xia Zhao received her Ph.D. degree from the School of Automation, Guangdong University of Technology, Guangzhou, China, in 2024. She now works at Guangzhou Railway Polytechnic, Guangzhou, China. Her research interests include synchronization and tracking control about complex dynamic networks.

Yin-he Wang received his Ph.D. degree in control theory and engineering from Northeastern University, Shenyang, China, in 1999. From 2000 to 2002, he was a Post-doctor in Department of Automatic control, Northwestern Polytechnic University, Xi’an, China. From 2005 to 2006, he was a visiting scholar at Department of Electrical Engineering, Lakehead University, Canada. He is currently a Professor with the School of Automation, Guangdong University of Technology, Guangzhou, China. His research interests include fuzzy adaptive robust control, analysis for nonlinear systems, and complex dynamical networks.

Pei-tao Gao received his Ph.D. degree from the School of Automation, Guangdong University of Technology, Guangzhou, China, in 2023. He is currently an Associate Professor with the School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou, China. His research interests include tracking and synchronization control for complex dynamical networks.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Jx., Wang, Yh. & Gao, Pt. Asymptotical Tracking Control of Complex Dynamical Network Based on Links State Observer. Int. J. Control Autom. Syst. (2024). https://doi.org/10.1007/s12555-023-0626-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12555-023-0626-x

Keywords

Search

Navigation