Advertisement

Robust Stochastic Sampled-data-based Output Consensus of Heterogeneous Multi-agent Systems Subject to Random DoS Attack: A Markovian Jumping System Approach

  • Hongjie Ni
  • Zhenhua Xu
  • Jun ChengEmail author
  • Dan Zhang
Article
  • 7 Downloads

Abstract

This paper addresses the robust stochastic sampled-data-based output feedback (SSDBOF) consensus controller design for a network of continuous-time heterogeneous multi-agent systems (MASs) in the presence of denial-of-service (DoS) attack. Under the mild assumption that the sampling instant is stochastically triggered and satisfies the Markov property, a homogeneous Markovian jump system (MJS) method is introduced that is capable of modeling the stochastic sampled-data-based control system. Furthermore, the randomly occurring Deny-of-Service (DoS) attack problem is also taken into account due to the existence of potential adversary that tries to block the communication channels. A novel discrete-time stochastic Markovian system model is first introduced that enables us to deal with the stochastic sampling and random DoS attack phenomena in a unified framework. Then by adopting the decoupling scheme, some sufficient conditions are proposed such that all the outputs of the following agents can track the output of the leading agent, and the prescribed H performance level is also guaranteed. In our work, the SSDBOF consensus controller design method is transformed to a feasibility problem subject to the linear matrix inequality (LMI) constraints. The theoretical results are finally applied to solve the position tracking problem of a network of vehicle systems.

Keywords

Distributed control LMI Markovian jump systems multi-agent systems robust control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Que, M. Fang, Z. G. Wu, H. Su, T. Huang, and D. Zhang, “Exponential synchronization via aperiodic sampling of complex delayed networks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI: 10.1109/tsmc.2018.2858247Google Scholar
  2. [2]
    W. Zhang, and L. Shi, “Sequential fusion estimation for clustered sensor networks,” Automatica, vol. 89, pp. 358–363, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    H. Wang, C. Zhang, Y. Song, and B. Pang, “Masterfollowed multiple robots cooperation SLAM adapted to search and rescue environment,” International Journal of Control, Automation and Systems, vol. 16, no. 6, pp. 2593–2608, 2018.CrossRefGoogle Scholar
  4. [4]
    D. Zhang, Z. H. Xu, H. R. Karimi, and Q. G. Wang, “Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization,” IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 64, no. 10, pp. 2783–2796, 2017.CrossRefGoogle Scholar
  5. [5]
    F. Guo, Q. Xu, C. Wen, L. Wang, and P. Wang, “Distributed secondary control for power allocation and voltage restoration in islanded DC microgrids,” IEEE Transactions on Sustainable Energy, vol. 9, no. 4, pp. 1857–1869, 2018.CrossRefGoogle Scholar
  6. [6]
    D. Zhang, S. K. Nguang, D. Srinivasan, and L. Yu, “Distributed filtering for discrete-time T-S fuzzy systems with incomplete measurements,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 3, pp. 1459–1471, 2018.CrossRefGoogle Scholar
  7. [7]
    Y. Hong, G. Chen, and L. Bushnell, “Distributed observers design for leader-following control of multi-agent networks,” Automatica, vol. 44, no. 3, pp. 846–850, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    W. Zhu, and D. Cheng, “Leader-following consensus of second-order agents with multiple time-varying delays,” Automatica, vol. 46, no. 12, pp. 1994–1999, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    C. Y. Han and W. Wang, “Distributed observer-based LQ controller design and stabilization for discrete-time multiagent systems,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1765–1774, 2018.MathSciNetCrossRefGoogle Scholar
  10. [10]
    X. Dong, Y. Zhou, Z. Ren, and Y. Zhong, “Timevarying formation tracking for second-order multi-agent systems subjected to switching topologies with application to quadrotor formation flying,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 5014–5024, 2017.CrossRefGoogle Scholar
  11. [11]
    D. D. Zhao, T. Dong, and W. J. Hu, “Event-triggered consensus of discrete time second-order multi-agent network,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 87–96, 2018.CrossRefGoogle Scholar
  12. [12]
    X. Dong, and G. Hu, “Time-varying formation tracking for linear multi-agent systems with multiple leaders,” IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3658–3664, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    X. Dong and G. Hu, “Time-varying formation control for general linear multi-agent systems with switching directed topologies,” Automatica, vol. 73, pp. 47–55, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Y.W.Wang, X. K. Liu, J.W. Xiao, and Y. J. Shen, “Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control,” Automatica, vol. 93, pp. 26–32, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Y. Su and J. Huang, “Cooperative output regulation of linear multi-agent systems,” IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 1062–1066, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    X. Dong, Q. Li, Z. Ren, and Y. Zhong, “Output formationcontainment analysis and design for general linear timeinvariant multi-agent systems,” Journal of the Franklin Institute, vol. 353, no. 2, pp. 322–344, 2016.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Z. Li, R.Wei, X. Liu, and M. Fu, “Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders,” International Journal of Robust and Nonlinear Control, vol. 23, no. 5, p. 534–547, 2013.Google Scholar
  18. [18]
    D. Zhang, Z. Xu, H. Karimi, Q. Wang, and L. Yu, “Distributed H¥ output-feedback control for consensus of heterogeneous linear multiagent systems with aperiodic sampled-data communications,” IEEE Transactions on Industrial Electronics, vol. 65, no. 6, pp. 4145–4155, 2018.CrossRefGoogle Scholar
  19. [19]
    J. Xu, L. Xie, T. Li, and K. Y. Lum, “Consensus of multiagent systems with general linear dynamics via dynamic output feedback control,” IET Control Theory and Applications, vol. 7, no. 1, pp. 108–115, 2013.MathSciNetCrossRefGoogle Scholar
  20. [20]
    X.Wang, L. Cheng, Z. Q. Cao, C. Zhou, M. Tan, and Z. G. Hou, “Output-feedback consensus control of linear multiagent systems: a fixed topology,” International Journal of Innovative Computing Information and Control, vol. 7, no. 5, pp. 2063–2074, 2011.Google Scholar
  21. [21]
    Z. H. Wang, H.S. Zhang, X. M. Song, and H. X. Zhang, “Consensus problems for discrete-time agents with communication delay,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1515–1523, 2017.CrossRefGoogle Scholar
  22. [22]
    Q. Jiao, H. Zhang, S. Xu, F. L. Lewis, and L. Xie, “Bipartite tracking of homogeneous and heterogeneous linear multi-agent systems,” International Journal of Control, 2018. DOI: 10.1080/00207179.2018.1467044Google Scholar
  23. [23]
    G. Wen, Y. Zhao, Z. Duan, W. Yu, and G. Chen, “Containment of higher-order multi-leader multi-agent systems: a dynamic output approach,” IEEE Transactions on Automatic Control, vol. 61, no. 4, pp. 1135–1140, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    F.Y. Wang, Z. X. Liu, and Z. Q. Chen, “A novel leaderfollowing consensus of multi-agent systems with smart leader,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1483–1492, 2018.CrossRefGoogle Scholar
  25. [25]
    M. Fan and Y. Wu, “Global leader-following consensus of nonlinear multi-agent systems with unknown control directions and unknown external disturbances,” Applied Mathematics and Computation, vol. 331, pp. 274–286, 2018.MathSciNetCrossRefGoogle Scholar
  26. [26]
    Q. Jiao, H. Modares, F. L. Lewis, S. Xu, and L. Xie, “Distributed l2-gain output-feedback control of homogeneous and heterogeneous systems,” Automatica, vol. 71, pp. 361–368, 2016.CrossRefzbMATHGoogle Scholar
  27. [27]
    Z. Li, Z. Duan, and F. L. Lewis, “Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties,” Automatica, vol. 50, no. 3, pp. 883–889, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    H. Cai, F. Lewis, G. Hu, and J. Huang, “The adaptive distributed observer approach to the cooperative output regulation of linear multi-agent systems,” Automatica, vol. 75, pp. 299–305, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    J. Kim, J. Yang, H. Shim, J. S. Kim, and H. S. Jin, “Robustness of synchronization of heterogeneous agents by strong coupling and a large number of agents,” IEEE Transactions on Automatic Control, vol. 61, no. 10, pp. 3096–3102, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Y. Wu, R. Lu, P. Shi, H. Su, and Z. Wu, “Analysis and design of synchronization for heterogeneous network,” IEEE Transactions on Cybernetics, vol. 48, no. 4, pp. 1253–1262, 2018.CrossRefGoogle Scholar
  31. [31]
    Y. Wu, H. R. Karimi, and R. Lu, “Sampled-data control of network systems in industrial manufacturing,” IEEE Transactions on Industrial Electronics, vol. 64, no. 11, pp. 9016–9024. 2018.CrossRefGoogle Scholar
  32. [32]
    Y.Wu, R. Lu, P. Shi, H. Su, and Z. Wu, “Sampled-data synchronization of complex networks with partial couplings and T-S fuzzy nodes,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 782–793, 2018.CrossRefGoogle Scholar
  33. [33]
    Y. Y. Wang, H. Shen, and D. P. Duan, “On stabilization of quantized sampled-data neural-network-based control systems,” IEEE Transactions on Cybernetics, vol. 47, no. 10, pp. 3124–3135, 2017.CrossRefGoogle Scholar
  34. [34]
    Y. Y. Wang, Y. Q. Xia, and P. F. Zhou, “Fuzzymodel-based sampled-data control of chaotic systems: a fuzzy time-dependent Lyapunov-Krasovskii functional approach,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 6, pp. 1672–1684, 2017.CrossRefGoogle Scholar
  35. [35]
    J. Cheng, J. H. Park, H. R. Karimi, and H. Shen, “A flexible terminal approach to sampled-data exponentially synchronization of Markovian neural networks with time-varying delayed signals,” IEEE Transactions on Cybernetics, vol. 48, no. 8, pp. 2232–2244, 2018.CrossRefGoogle Scholar
  36. [36]
    D. Zhang, P. Shi, and L. Yu, “Containment control of linear multiagent systems with aperiodic sampling and measurement size reduction,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 10, pp. 5020–5029, 2018.MathSciNetCrossRefGoogle Scholar
  37. [37]
    Z. G. Ma, Z. X. Liu, and Z. Q. Chen, “Modified leaderfollowing consensus of time-delay multi-agent systems via sampled control and smart leader,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2526–2537, 2017.CrossRefGoogle Scholar
  38. [38]
    D. Zeng, R. Zhang, X. Liu, S. Zhong, and K. Shi, “Pinning stochastic sampled-data control for exponential synchronization of directed complex dynamical networks with sampled-data communications,” Applied Mathematics and Computation, vol. 337, pp. 102–118, 2018.MathSciNetCrossRefGoogle Scholar
  39. [39]
    H. Ni, Z. Xu, D. Zhang, and L. Yu, “Output feedback control of heterogeneous multi-agent systems with stochastic sampled-data,” Proceeding of the Chinese Automation Congress, Jinan, China, 2017.Google Scholar
  40. [40]
    W. He, B. Zhang, Q. L. Han, F. Qian, J. Kurths, and J. Cao, “Leader-following consensus of nonlinear multiagent systems with stochastic sampling,” IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 327–338, 2017.Google Scholar
  41. [41]
    D. Zhang, Z. Xu, D. Srinivasan, and L. Yu, “Leaderfollower consensus of multiagent systems with energy constraints: a Markovian system approach,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 7, pp. 1727–1736, 2017.CrossRefGoogle Scholar
  42. [42]
    Y. Yuan, F. C. Sun, and Q, Y. Zhu, “Resilient control in the presence of DoS attack: switched system approach,” International Journal of Control, Automation and Systems, vol. 13, no. 6, pp. 1423–1435, 2015.CrossRefGoogle Scholar
  43. [43]
    Y. Yuan, and F. C. Sun, “Data fusion-based resilient control system under DoS attacks: a game theoretic approach,” International Journal of Control, Automation and Systems, vol. 13, no. 3, pp. 513–520, 2015.CrossRefGoogle Scholar
  44. [44]
    Z. Feng, G. Hu, and G. Wen, “Distributed consensus tracking for multi-agent systems under two types of attacks,” International Journal of Robust and Nonlinear Control, vol. 26, no. 5, pp. 896–918, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    D. Ding, Z. Wang, D.W. Ho, and G. Wei, “Observer-based event-triggering consensus control for multiagent systems with lossy sensors and cyber-attacks,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1936–1947, 2017.CrossRefGoogle Scholar
  46. [46]
    D. Zhang, L. Liu, and G. Feng, “Consensus of heterogeneous linear multiagent systems subject to aperiodic sampled-data and DoS attack,” IEEE Transactions on Cybernetics, 2018. DOI: 10.1109/TCYB.2018.2806387Google Scholar
  47. [47]
    v J. Xi, Z. Shi, and Y. Zhong, “Consensus analysis and design for highorderlinear swarm systems with time-varying delays,” Physica A: Statistical Mechanics and its Applications, vol. 390, Nos. 23–24, pp. 4114–4123, 2011.CrossRefGoogle Scholar
  48. [48]
    L. Zhang, and E. K. Boukas, “Mode-dependent H¥ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities,” Automatica, vol. 45, no. 6, pp. 1462–1467, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    P. Wiel, R. Sepulchre, and F. Allgower, “An internal model principle is necessary and sufficient for linear output synchronization,” Automatica, vol. 47, no. 5, pp. 1068–1074, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    Y. Liu, J. H. Park, B. Guo, and Y. Shu, “Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 1040–1045, 2018.CrossRefGoogle Scholar
  51. [51]
    Y. Y. Wang, H. R. Karimi, H. K. Lam, and H. Shen, “An improved result on exponential stabilization of sampleddata fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 6, pp. 3875–3883, Dec. 2018.CrossRefGoogle Scholar
  52. [52]
    Y. Y. Wang, H. R. Karimi, H. Shen, Z. J. Fang, and M. X. Liu, “Fuzzy-model-based sliding mode control of nonlinear descriptor systems,” IEEE Transactions on Cybernetics, 2018. DOI: 10.1109/TCYB.2018.2842920Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Information EngineeringZhejiang University of TechnologyHangzhouP. R. China
  2. 2.School of Automation and Electrical EngineeringQingdao University of Science and TechnologyQingdaoP. R. China
  3. 3.School of ScienceHubei University for NationalitiesEnshi, HubeiP. R. China

Personalised recommendations