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Event-triggering Consensus for Second-order Leader-following Multiagent Systems with Nonlinear Time-delayed Dynamics

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  • Control Theory and Applications
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Abstract

This work focuses on the leader-following consensus problem for networks of dynamic agents, each of which has second-order nonlinear time-delayed dynamics. Event-triggered control and pinning control strategies are used in view of energy conservation. For each agent, the controller updates only when a properly presented event triggering condition is satisfied, which is based on the measurement errors and an exponential term. The network communication topology contains a directed spanning tree and only a fraction of follower agents can obtain the leader agent’s information. By virtue of the Lyapunov-Krasovskii functional method, the M-matrix theory and some algebraic inequalities, a sufficient condition for achieving leader-following consensus is established. The Zeno-behavior of triggered time sequence is excluded whether the consensus is reached or not. Finally, a simulation example is provided to demonstrate the proposed theoretical results.

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References

  1. A. Jadbabaue, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbors rules,” IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 998–1001, June 2003.

    MathSciNet  Google Scholar 

  2. B. D. A. Anderson, B. Fidan, C. B. Yu, and D. Walle, “UAV formation control: theory and application,” in Recent Advances in Learning and Control, Springer, London, pp. 15–33, January 2008.

    Chapter  Google Scholar 

  3. M. Chadli, M. Davoodi, and N. Meskin, “Distributed state estimation, fault detection and isolation filter design for heterogeneous multi-agent linear parameter-varying systems,” IET Control Theory and Applications, vol. 11, no. 2, pp. 254–262, January 2017.

    Article  MathSciNet  Google Scholar 

  4. Y. Cao, D. Stuart, W. Ren, and Z. Meng, “Distributed contaunment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments,” IEEE Transactions on Control Systems Technology, vol. 19, no. 4, pp. 929–938, July 2011.

    Article  Google Scholar 

  5. A. Albert and B. G. Robert, “Comparison of event-triggered and time-triggered concepts with regard to distributed control systems,” Embedded World, pp. 235–252, January 2004.

  6. S. P. Wen, Z. G. Zeng, and T. W. Huang, “Event-based control for memristive systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 10, pp. 3431–3443, October 2014.

    Article  MathSciNet  Google Scholar 

  7. J. L. Liu, L. L. Wei, X. P. Xie, and D. Yue, “Distributed event-triggered state estimators design for networked sensor systems with deception attacks,” IET Control Theory and Applications, 2018. DOI: 10.1049/iet-cta.2018.5868

    Article  Google Scholar 

  8. Z. R. Hu, P. Shi, L. G. Wu, and C. K. Ahn, “Event-based distributed filtering approach to nonlinear stochastic systems over sensor networks,” International Journal of Control, Automation and Systems, vol. 17, no. 4, pp. 896–906, March 2019.

    Article  Google Scholar 

  9. J. L. Liu, E. G. Tian, X. P. Xie, and L. Hong, “Distributed event-triggered control for networked control systems with stochastic cyber-attacks,” Journal of the Franklin Institute, March 2018. DOI: 10.1016/j.jfranklin.2018.01.048

    Article  MathSciNet  Google Scholar 

  10. Y. Xu, M. Fang, Z. G. Wu, Y. J. Pan, M. Chadli, and T. W. Huang, “Input-based event-triggering consensus of multiagent systems under denial-of-service attacks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: 10.1109/TSMC.2018.2875250

  11. W. Zhu, Z. P. Jiang, and G. Feng, “Event-based consensus of multi-agent systems with general linear models,” Automatica, vol. 50, no. 2, pp. 552–558, February 2014.

    Article  MathSciNet  Google Scholar 

  12. L. L. Li, D. Ho, and J. Q. Lu, “Event-based network consensus with communication delays,” Nonlinear Dynamics, vol. 87, no. 3, pp. 1847–1858, February 2017.

    Article  Google Scholar 

  13. W. F. Hu, L. Liu, and G. Feng, “Consensus of linear multi-agent systems by distributed event-triggered strategy,” IEEE Transactions on Cybernetics, vol. 46, no. 1, pp. 148–157, January 2016.

    Article  Google Scholar 

  14. Z. K. Tang, “Event-triggered consensus of linear discrete-time multi-agent systems with time-varying topology,” International Journal of Control Automation and Systems, vol. 16, no. 3, pp. 1179–1185, June 2018.

    Article  Google Scholar 

  15. K. X. Liu, P. H. Duan, Z. S. Duan, H. B. Cau, and J. H. Lü, “Leader-following consensus of multi-agent systems with switching networks and event-triggered control,” IEEE Transactions on Circuits and Systems I Regular Papers, vol. 99, pp. 1–11, October 2017.

    Article  Google Scholar 

  16. W. C. Zou and Z. R. Xiang, “Event-triggered leader-following consensus of non-linear multi-agent systems with switched dynamics,” IET Control Theory and Applications, vol. 13, no. 9, pp. 1222–1228, June 2019.

    Article  MathSciNet  Google Scholar 

  17. M. Rehan, C. K. Ahn and M. Chadli, “Consensus of one-sided Lipschitz multi-agents under input saturation” IEEE Transactions on Circuits and Systems II: Express Briefs, 2019. DOI: 10.1109/TCSII.2019.2923721

  18. M. Cao, A. Morse, and B. Anderson, “Reaching a consensus in a dynamically changing environment: a graphical approach,” SIAM Journal on Control and Optimization, vol. 47, no. 2, pp. 575–600, January 2008.

    Article  MathSciNet  Google Scholar 

  19. W. Ren, “Synchronization of coupled harmonic oscillators with local interaction,” Automatica, vol. 44, no. 12, pp. 3195–3200, December 2008.

    Article  MathSciNet  Google Scholar 

  20. H. Khalil and J. Grizzle, Nonlinear Systems, Prentice Hall, Upper Saddle River, 2002.

    Google Scholar 

  21. D. X. Wang, Y. B. Cheng, and S. Z. Ying, “Time-varying formation control for unmanned aerial vehicles: theories and applications,” IEEE Transactions on Control Systems Technology, vol. 23, no. 1, pp. 340–348, March 2014.

    Google Scholar 

  22. S. Y. Xu, Y. Zou, D. S. Xie, and Z. Li, “Event-triggered consensus control for second-order multi-agent systems,” IET Control Theory and Applications., vol. 9, no. 5, pp. 667–680, March 2015.

    Article  MathSciNet  Google Scholar 

  23. M. Yu, C. Yan, and C. Li, “Event-triggered control for heterogeneous multi-agent systems with time-varying delays when using the second-order neighbours’ information,” International Journal of Automation and Control, vol. 10, no. 3, pp. 286–307, July 2016.

    Article  Google Scholar 

  24. N. K. Mu, X. F. Liao, and T. W. Huang, “Consensus of second-order multi-agent systems with random sampling via event-triggered control,” Journal of the Franklin Institute, vol. 353, no. 6, pp. 1423–1435, April 2016.

    Article  MathSciNet  Google Scholar 

  25. T. T. Xie, X. F. Liao, and H. Q. Li, “Leader-following consensus in second-order multi-agent systems with input time delay: an event-triggered sampling approach,” Neurocomputing, vol. 177, no. 12, pp. 130–135, February 2016.

    Article  Google Scholar 

  26. C. R. Jiang, H. B. Du, W. W. Zhu, L. S. Yin, X. Z. Jin, and G. H. Wen, “Synchronization of nonlinear networked agents under event-triggered control,” Information Science, vol. 459, pp. 317–326, August 2018.

    Article  MathSciNet  Google Scholar 

  27. A. Zhang, D. Zhou, P. Yang, and M. Yang, “Event-triggered finite-time consensus with fully continuous communication free for second-order multi-agent systems,” International Journal of Control, Automation and Systems, vol. 17, no. 4, pp. 836–846, March 2019.

    Article  Google Scholar 

  28. H. Q. Li, G. Chen, Z. Y. Dong, and D. W. Xia, “Consensus analysis of multiagent systems with second-order nonlinear dynamics and general directed topology: an event-triggered scheme,” Information Science, vol. 370–371, pp. 598–622, November 2016.

    Article  Google Scholar 

  29. H. Dau, W. S. Chen, J. Xie, and J. P. Jia, “Exponential synchronization for second-order nonlinear systems in complex dynamical networks with time-varying inner coupling via distributed event-triggered transmission strategy,” Nonlinear Dynamics, vol. 92, no. 3, pp. 853–867, May 2018.

    Article  Google Scholar 

  30. D. P. Li, L. Liu, Y. J. Liu, and S. C. Tong, “Adaptive NN control without feasibility conditions for nonlinear state constrauned stochastic systems with unknown time delays,” IEEE Transactions on Cybernetics, vol. 99, pp. 1–10, March 2019.

    Google Scholar 

  31. D. P. Li, C. L. P. Chen, Y. J. Liu, and S. C. Tong, “Neural network controller design for a class of nonlinear delayed systems with time-varying full-state constraunts,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–12, January 2019.

  32. D. P. Li, L. Liu, Y. J. Liu, and C. L. P. Chen, “Fuzzy approximation-based adaptive control of nonlinear uncertaun state constrauned systems with time-varying delays,” IEEE Transactions on Fuzzy Systems, vol. 99, pp. 1–12, May 2019.

    Google Scholar 

  33. Y. L. Wang, J. D. Cao, H. J. Wang, and F. E. Alsaadi, “Event-triggered consensus of multi-agent systems with nonlinear dynamics and communication delay,” Physica A, vol. 522, no. pp. 147–157, February 2019.

    Article  MathSciNet  Google Scholar 

  34. C. R. Jiang, H. B. Du, W. W. Zhu, L. S. Yin, X. Z. Jin, and G. H. Wen, “Synchronization of nonlinear networked agents under event-triggered control,” Information Sciences, vol. 459, pp. 317–326, August 2018.

    Article  MathSciNet  Google Scholar 

  35. H. Q. Li, X. F. Liao, G. Chen, D. J. Hill, Z. Y. Dong, and T. W. Huang, “Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks,” Neural Networks, vol. 66, pp. 1–10, June 2015.

    Article  Google Scholar 

  36. A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Science, Academic Press, 1979.

  37. Q. Song, F. Liu, J. Cao, and W. W. Yu, “Pinningcontrollability analysis of complex networks: an M-matrix approach,” IEEE Transactions on Circuits and Systems I Regular Papers, vol. 59, no. 11, pp. 2692–2701, November 2012.

    Article  MathSciNet  Google Scholar 

  38. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.

    Book  Google Scholar 

  39. P. Ioannou and B. Fidan, Adaptive Control Tutorial (Adavances in Design and Control), SIAM, Philadelphia, PA, 2006.

    Book  Google Scholar 

  40. Y. Fan, Y. Yang, and Y. Zhang, “Sampling-based event-triggered consensus for multi-agent systems,” Neurocomputing, vol. 191, pp. 141–147, May 2016.

    Article  Google Scholar 

  41. B. Zhou, X. F. Liao, T. W. Huang, and G. Chen, “Pinning exponential synchronization of complex networks via event-triggered communication with combinational measurements,” Neurocomputing, vol. 157, pp. 199–207, June 2015.

    Article  Google Scholar 

  42. Y. Cao, L. Y. Zhang, C. Y. Li, and M. Z. Q. Chen, “Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 2212–2222, August 2017.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing, 211171, China

    Yangling Wang

  2. Research Center for Complex Systems and Network Sciences, and the School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. School of Electronic Engineering, Nanjing Xiaozhuang University, Nanjing, 211171, China

    Haijun Wang

  4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fuad E. Alsaadi

Authors
  1. Yangling Wang
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  2. Jinde Cao
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  3. Haijun Wang
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  4. Fuad E. Alsaadi
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Correspondence to Yangling Wang.

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Recommended by Associate Editor M. Chadli under the direction of Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China under Grants 61703210 and 61573096.

Yangling Wang received her B.S. and M.S. degrees in mathematics and applied mathematics from Anhui Normal University, Wuhu, China, in 2002 and in 2005, respectively, and received her Ph.D. degree from Southeast University, Nanjing, China, in 2015. She is currently an associate professor in School of Information Engineering, Nanjing Xiaozhuang University, Nanjing, China. Her current research interests include stability theory of neural networks, consensus and synchronization of complex neural networks.

Jinde Cao received the B.S. degree from Anhui Normal University, Wuhu, China, the M.S. degree from Yunnan University, Kunming, China, and the Ph.D. degree from Sichuan University, Chengdu, China, all in mathematics/applied mathematics, in 1986, 1989, and 1998, respectively. He is an Endowed Chair Professor, the Dean of the School of Mathematics, the Director of the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence of China and the Director of the Research Center for Complex Systems and Network Sciences at Southeast University. Prof. Cao was a recipient of the National Innovation Award of China, Obada Prize and the Highly Cited Researcher Award in Engineering, Computer Science, and Mathematics by Thomson Reuters/Clarivate Analytics. He is elected as a fellow of IEEE, a member of the Academy of Europe, a member of the European Academy of Sciences and Arts, a fellow of Pakistan Academy of Sciences, and an IASCYS academician.

Haijun Wang is an associate professor in Nanjing Xiaozhuang University. From 1999, he has been engaged in teaching and research work in the Department of Physics, Nanjing Xiaozhuang University, Nanjing, China. His research field includes nonlinear system dynamics research of complex network, nonlinear optics, chaotic secure communication and computer assisted instruction.

Fuad E. Alsaadi received his B.S. and M.S. degrees in electronic and communication from King AbdulAziz University, Jeddah, Saudi Arabia, in 1996 and 2002. He then received his Ph.D. degree in Optical Wireless Communication Systems from the University of Leeds, Leeds, UK, in 2011. Between 1996 and 2005, he worked in Jeddah as a communication instructor in the College of Electronics and Communication. He was a lecturer in the Faculty of Engineering in King AbdulAziz University, Jeddah, Saudi Arabia in 2005. He is currently an associate professor of the Electrical and Computer Engineering Department within the Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia. He published widely in the top IEEE communications conferences and journals and has received the Carter award, University of Leeds for the best PhD. He has research interests in optical systems and networks, signal processing, network optimization, synchronization and systems design and control.

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Wang, Y., Cao, J., Wang, H. et al. Event-triggering Consensus for Second-order Leader-following Multiagent Systems with Nonlinear Time-delayed Dynamics. Int. J. Control Autom. Syst. 18, 1083–1093 (2020). https://doi.org/10.1007/s12555-019-0385-x

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