Influence Analysis of Leader Information with Application to Formation Control of Multi-agent Systems


Considering the problem that does all the information have the same effect on the control performance of multi-agent system, this paper analyzes the influence of leader state on closed loop dynamics of formation theoretically. For the first time, it is proved that the leader information can mask out the effect of others and the closed loop dynamics of formation is equivalent to the leader follower topology if all followers can receive the leader information and others. Based on this new foundation, an estimator for leader state is designed using the sliding mode control theory. This estimator is independent of the dynamical functions of agents and only the minimum eigenvalue of topological matrix is required to ensure the convergence of estimation error even when leader runs dynamically. Several simulations have been conducted to further validate the correctness of this new theoretical foundation and the effectiveness of the estimator based formation control strategy.

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  1. [1]

    J. Lagorse, D. Paire, and A. Miraoui, “A multi-agent system for energy management of distributed power sources,” Renewable Energy, vol. 35, no. 1, pp. 174–182, 2010.

    Article  Google Scholar 

  2. [2]

    L. Hernandez, C. Baladron, J. M. Aguiar, and B. Carro, “A multi-agent system architecture for smart grid management and forecasting of energy demand in virtual power plants,” IEEE Communications Magazine, vol. 51, no. 1, pp. 106–113, 2013.

    Article  Google Scholar 

  3. [3]

    I. Arel, C. Liu, T. Urbanik, and A. G. Kohls, “Reinforcement learning-based multi-agent system for network traffic signal control,” IET Intelligent Transport Systems, vol. 4, no. 2, pp. 128–135, 2010.

    Article  Google Scholar 

  4. [4]

    K. Li, S. E. Li, F. Gao, Z. Lin, and Q. Sun, “Robust distributed consensus control of uncertain multi-agents interacted by eigenvalue-bounded topologies,” IEEE Internet of Things Journal, 2020. DOI:

  5. [5]

    P. Dasgupta, “A multi-agent swarming system for distributed automatic target recognition using unmanned aerial vehicles,” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, vol. 38, no. 3, pp. 549–563, 2008.

    Article  Google Scholar 

  6. [6]

    M. Yan, W. Ma, L. Zuo, and P. Yang, “Dual-mode distributed model predictive control for platooning of connected vehicles with nonlinear dynamics,” International Journal of Control Automation and Systems, vol. 17, no. 12, pp. 3091–3101, 2019.

    Article  Google Scholar 

  7. [7]

    Q. Xia, F. Gao, J. Duan, and Y. He, “Decoupled H control of automated vehicular platoons with complex interaction topologies,” IET Intelligent Transport Systems, vol. 11, no. 2, pp. 92–101, 2017.

    Article  Google Scholar 

  8. [8]

    K. K. Oh, M. C. Park, and H. S. Ahn, “A survey of multiagent formation control,” Automatica, vol. 53, pp. 424–440, 2015.

    MathSciNet  MATH  Article  Google Scholar 

  9. [9]

    F. Gao, X. Hu, S. E. Li, K. Li, and Q. Sun, “Distributed adaptive sliding mode control of vehicular platoon with uncertain interaction topology,” IEEE Transactions on Industrial Electronics, vol. 65, no. 8, pp. 6352–6361, 2018.

    Article  Google Scholar 

  10. [10]

    C. E. Ren and C. L. P. Chen, “Sliding mode leader-following consensus controllers for second-order nonlinear multi-agent systems,” IET Control Theory & Applications, vol. 9, no. 10, pp. 1544–1552, 2015.

    MathSciNet  Article  Google Scholar 

  11. [11]

    H. Li, L. Xu, L. Xiao, and L. Li, “Second-order leader-following consensus of nonlinear multi-agent systems via adaptive pinning control,” Proc. of the 26th Chinese Control & Decision Conference, 2014.

  12. [12]

    F. Gao, D. Dang, Y. He, and Q. Hu, “Distributed H control of AVs interacted by uncertain and switching topology in a platoon,” Journal of Advanced Transportation, vol. 2019, Article ID: 9723042, 2019.

  13. [13]

    J. A. Fax and R. M. Murray, “Influence flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol. 49, no. 1, pp. 115–120, 2004.

    MathSciNet  MATH  Article  Google Scholar 

  14. [14]

    N. I. Wei and D. Cheng, “Leader-following consensus of multi-agent systems under fixed and switching topologies,” Systems & Control Letters, vol. 59, no. 3, pp. 209–217, 2010.

    MathSciNet  MATH  Google Scholar 

  15. [15]

    J. Wang, D. Cheng, and X. Hu, “Consensus of multi-agent linear dynamic systems,” Asian Journal of Control, vol. 10, no. 2, pp. 144–155, 2010.

    MathSciNet  Article  Google Scholar 

  16. [16]

    H. Jiang, J. Yu, and C. Zhou, “Consensus of multi-agent linear dynamic systems via impulsive control protocols,” International Journal of Systems Science, vol. 42, no. 6, pp. 967–976, 2011.

    MathSciNet  MATH  Article  Google Scholar 

  17. [17]

    Y. Lv, Z. Li, and Z. Duan, “Adaptive output-feedback consensus protocol design for linear multi-agent systems with directed graphs,” Proc. of Control & Decision Conference, 2015.

  18. [18]

    Y. Lv, Z. Li, and Z. Duan, “Distributed adaptive consensus protocols for linear multi-agent systems over directed graphs with relative output information,” IET Control Theory & Applications, vol. 12, no. 5, pp. 613–620, 2017.

    MathSciNet  Article  Google Scholar 

  19. [19]

    C. Tan, G. P. Liu, and G. R. Duan, “Group consensus of networked multi-agent systems with directed topology,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 8878–8883, 2011.

    Article  Google Scholar 

  20. [20]

    S. E. Li, F. Gao, K. Li, L. Wang, K. Xu, and D. Cao, “Robust longitudinal control of multi-vehicle systems-a distributed H-infinity method,” IEEE Transactions on Intelligent Transportation Systems, vol. 19, no. 9, pp. 2779–2788, 2018.

    Article  Google Scholar 

  21. [21]

    X. Wang and G. H. Yang, “Adaptive reliable coordination control for linear agent networks with intermittent communication constraints,” IEEE Transactions on Control of Network Systems, vol. 5, no. 3, pp. 1120–1131, 2017.

    MathSciNet  MATH  Article  Google Scholar 

  22. [22]

    X. Wang and G. H. Yang, “Fault-tolerant consensus tracking control for linear multi-agent systems using switching directed network,” IEEE Transactions on Cybernetics, 2019. DOI:

  23. [23]

    A. A. Peters, R. H. Middleton, and O. Mason, “Leader tracking in homogeneous vehicle platoons with broadcast delays,” Automatica, vol. 50, pp. 64–74, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  24. [24]

    J. Gong, Y. Zhao, and Z. Lu, “Sampled-data vehicular platoon control with communication delay,” System Control Engineering, vol. 232, pp. 39–49, 2017.

    Google Scholar 

  25. [25]

    F. Gao, S. E. Li, Y. Zheng, and D. Kum, “Robust control of heterogeneous vehicular platoon with uncertain dynamics and communication delay,” IET Intelligent Transport Systems, vol. 10, pp. 503–513, 2016.

    Article  Google Scholar 

  26. [26]

    K. Subramanian, P. Muthukumar, and Y. H. Joo, “Leader-following consensus of nonlinear multi-agent systems via reliable Control with time-varying communication delay,” International Journal of Control Automation and Systems, vol. 17, no. 2, pp. 298–306, 2019.

    Article  Google Scholar 

  27. [27]

    B. Liu, F. Gao, Y. He, and C. Wang, “Robust control of heterogeneous vehicular platoon with non-ideal communication,” Electronics, vol. 8, no. 2, pp. 207–221, 2019.

    Article  Google Scholar 

  28. [28]

    S. E. Shladover, C. A. Desoer, J. K. Hedrick, M. Tomizuke, J. Walrand, W.-B. Zhang, D. H. McMahon, H. Peng, S. Sheikholeslam, and N. McKeown, “Automated vehicle control developments in the PATH program,” IEEE Transactions on Vehicular Technology, vol. 40, no. 1, pp. 114–130, 1991.

    Article  Google Scholar 

  29. [29]

    Z. Yang, S. E. Li, J. Wang, D. Cao, and K. Li, “Stability and scalability of homogeneous vehicular platoon: study on the influence of information flow topologies,” IEEE Transactions on Intelligent Transportation Systems, vol. 17, no. 1, pp. 14–26, 2015.

    Google Scholar 

  30. [30]

    Y. Yu, N. Li, L. Sun, J. Liu, and C. Sun, “Robust output feedback consensus of high-order multi-agent systems with nonlinear uncertainties,” International Journal of Control Automation and Systems, vol. 18, no. 2, pp. 282–292, 2020.

    Article  Google Scholar 

  31. [31]

    J. Duan, F. Gao, and Y. He, “Test scenario generation and optimization technology for intelligent driving systems,” IEEE Intelligent Transportation Systems Magazine, 2020. DOI:

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Corresponding author

Correspondence to Feng Gao.

Additional information

Recommended by Associate Editor Xiaojie Su under the direction of Editor Guang-Hong Yang.

This study is supported by Scientific Technological Plans of Chongqing under grant cstc2019jcyj-zdxmX0018 and Open fund of State Key Laboratory of Vehicle NVH and Safety Technology under grant NVHSKL-201705.

Bo He received his M.S. degree in Control Engineering from Chongqing University of Posts and Telecommunications in 2015. From 2009 to 2014, he was engaged in Development and Matching of Control Logic for Engine Control System, and responsible for the matching of the first turbocharged engine and electronic thermostat (D18T) of Chang’an Automobile, the matching of the first phase sensor cancelled phase sensor engine (EA12) of Chang’an Automobile, etc. His current research interests include testing, validation, matching and evaluation of intelligent driving system (Advanced Driving Assistance and L3/L4 Auto-Driving).

Feng Gao received his M.S. and Ph.D. degrees from Tsinghua University, in 2003 and 2007, respectively. From 2007 to 2013, he was a Senior Engineer with the Chang’an Auto Global Research and Development Centre, where he has led several projects involving electromagnetic compatibility, durability test of electronic module, ADAS, and engine control. He is currently a Professor with the School of Automotive Engineering, Chongqing University. He is the author of over 80 peerreviewed journal and conference papers, and the co-inventor of over 20 patents in China. His current research interests include robust control and optimization approach with application to automotive systems. Prof. Gao was the recipient of Best Award of Automatic Driving Technology of International Intelligent Industry Expo. (2018), Technical Progress Award of Automotive Industry (2017, 2018), Special Application Award of NI Graphical System Design (2015) and Best Paper Award of Chongqing Electric Motor Society (2016).

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He, B., Gao, F. Influence Analysis of Leader Information with Application to Formation Control of Multi-agent Systems. Int. J. Control Autom. Syst. 18, 3062–3072 (2020).

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  • Decoupling analysis
  • formation control
  • multi-agent system
  • state estimation