Skip to main content
SpringerLink
Log in

Stability Analysis and Group Consensus Tracking Predictive Control of Multi-Agent Systems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The issue of stability and group consensus tracking is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints (e.g., time delays and data loss) in this paper. Firstly, the couple-group consensus tracking control is analyzed theoretically, the communication constraints are compensated by the prediction method, and the factor of leaders is introduced to make the system not lose generality. Secondly, the necessary and sufficient condition is given to ensure the stability of the system and achieve the couple-group consensus tracking control, and relax the topology constraint of in-degrees balance by cooperative-competitive interactions. In addition, the result of couple groups is extended to multiple groups based on the predictive control protocol. Numerical simulations with Matlab show that the proposed networked predictive control can effectively overcome the network constraints, the dynamic performance and control effect are better than the general control without the prediction.

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

Access this article

Log in via an institution

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. Wang Y L, Group consensus in multi-agent systems with switching topologies and communication delays, Systems & Control Letters, 2010, 59(6): 340–348.

    Article  MathSciNet  MATH  Google Scholar 

  2. Sankey D W E, Shepard E L C, Biro D, et al., Speed consensus and the ‘Goldilocks principle’ in flocking birds (Columba livia), Animal Behaviour, 2019, 157: 105–119.

    Article  Google Scholar 

  3. Lima S L and Lee J K, Is social coordination during escape flights a general phenomenon in birds?, Ethology, 2020, 126(1): 40–50.

    Article  Google Scholar 

  4. Sakamoto T, Bonardi S, and Kubota T, A routing framework for heterogeneous multi-robot teams in exploration tasks, IEEE Robotics and Automation Letters, 2020, 5(4): 6662–6669.

    Article  Google Scholar 

  5. Jiang Y, Ji L, Liu Q, et al., Couple-group consensus for discrete-time heterogeneous multiagent systems with cooperative-competitive interactions and time delays, Neurocomputing, 2018, 319(30): 92–101.

    Article  Google Scholar 

  6. Gao Y, Yu J, Yu M, et al., Couple-group consensus for second-order multi-agent systems with the effect of second-order neighbours’ information, Transactions of the Institute of Measurement and Control, 2017, 40(5): 1726–1737.

    Article  Google Scholar 

  7. An B R, Liu G P, and Tan C, Group consensus control for networked multi-agent systems with communication delays, ISA Transactions, 2018, 76: 78–87.

    Article  Google Scholar 

  8. Yang R T, Peng L, and Zhao H R, Scaled bipartite consensus controller design for second-order multi-agent systems with mixed time-delays, Journal of Systems Science & Complexity, 2022, 35(3): 888–908.

    Article  MathSciNet  MATH  Google Scholar 

  9. Li J, Guan Z H, and Chen G R, Multi-consensus of nonlinearly networked multi-agent systems, Asian Journal of Control, 2018, 17(1): 157–164.

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang X and Fan X, A distributed formation control scheme with obstacle avoidance for multiagent systems, Mathematical Problems in Engineering, 2019, 2019(1): 1–16.

    MathSciNet  MATH  Google Scholar 

  11. Yu J and He L, Scaled group consensus in agent networks with finite sub-networks under continuous/discrete-time settings, Journal of the Franklin Institute, 2018, 355(17): 8780–8801.

    Article  MathSciNet  MATH  Google Scholar 

  12. Qiao Z Y, Liu Y C, Wang X, Multi-cluster flocking behavior analysis for a delayed cucker-smale model with short-range communication weight, Journal of Systems Science & Complexity, 2022, 35(1): 137–158.

    Article  MathSciNet  MATH  Google Scholar 

  13. Couzin I, Krause J, Franks N R, et al., Effective leadership and decision-making in animal groups on the move, Nature, 2005, 433(7025): 513–516.

    Article  Google Scholar 

  14. Mateo D, Horsevad N, Hassani V, et al., Optimal network topology for responsive collective behavior, Science Advances, 2019, 5(4): eaau0999.

    Article  Google Scholar 

  15. Hua C C, You X, and Guan X P, Leader-following consensus for a class of high-order nonlinear multi-agent systems, Automatica, 2016, 73: 138–144.

    Article  MathSciNet  MATH  Google Scholar 

  16. Hua C C, Li K, and Guan X P, Leader-following output consensus for high-order nonlinear multi-agent systems, IEEE Transactions on Automatic Control, 2019, 64(3): 1156–1161.

    Article  MathSciNet  MATH  Google Scholar 

  17. Li K, Hua C C, You X, et al. Leader-following asynchronous consensus for multi-agent systems with unknown control and output directions, Automatica, 2021, 132: 109832.

    Article  MATH  Google Scholar 

  18. Chen L K, Guo L X, and Yang Y Q, Projective group consensus of multi-agent systems with arbitrary parameter, Journal of Systems Science & Complexity, 2021, 34(2): 618–631.

    Article  MathSciNet  MATH  Google Scholar 

  19. Li Y F, Park J H, Hua C C, et al., Distributed adaptive output feedback containment control for time-delay nonlinear multiagent systems, Automatica, 2021, 127: 109545.

    Article  MathSciNet  MATH  Google Scholar 

  20. Feng Y and Zheng W X, Group consensus control for discrete-time heterogeneous first- and second-order multi-agent systems, IET Control Theory and Applications, 2018, 12(6): 753–760.

    Article  MathSciNet  Google Scholar 

  21. Franchi A, Giordano P R, and Michieletto G, Online leader selection for collective tracking and formation control: The second order case, IEEE Transactions on Control of Network Systems, 2019, 6(4): 1415–1425.

    Article  MathSciNet  MATH  Google Scholar 

  22. Ma Q, Wang Z, and Miao G, Second-order group consensus for multi-agent systems via pinning leader-following approach, Journal of the Franklin Institute, 2014, 351(3): 1288–1300.

    Article  MATH  Google Scholar 

  23. Cui Q, Xie D, and Jiang F, Group consensus tracking control of second-order multi-agent systems with directed fixed topology, Neurocomputing, 2016, 218(7): 286–295.

    Article  Google Scholar 

  24. Zhang W and Liu J, Cooperative global robust group output regulation for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics, Nonlinear Dynamics, 2018, 92(4): 1733–1744.

    Article  MATH  Google Scholar 

  25. Xie D M, Shi L, and Jiang F C, Group tracking control of second-order multi-agent systems with fixed and Markovian switching topologies, Neurocomputing, 2018, 281: 37–46.

    Article  Google Scholar 

  26. Qin J and Yu C, Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition, Automatica, 2013, 49(9): 2898–2905.

    Article  MathSciNet  MATH  Google Scholar 

  27. Yu M, Yan C, and Li C, Event-triggered tracking control for couple-group multi-agent systems, Journal of the Franklin Institute, 2017, 354(14): 6152–6169.

    Article  MathSciNet  MATH  Google Scholar 

  28. Qin J, Ma Q, Yu X, et al., Output containment control for heterogeneous linear multi-agent systems with fixed and switching topologies, IEEE Transactions on Cybernetics, 2019, 49(12): 4117–4128.

    Article  Google Scholar 

  29. Pei H, Chen S, Lai Q, et al., Consensus tracking for heterogeneous interdependent group systems, IEEE Transactions on Cybernetics, 2020, 50(4): 1752–1760.

    Article  Google Scholar 

  30. Nejad H, Sugimura N, Iwamura K, et al., Multi-agent architecture for dynamic incremental process planning in the flexible manufacturing system, Journal of Intelligent Manufacturing, 2010, 21(4): 487–499.

    Article  Google Scholar 

  31. Lopez-Ortega O and Villar-Medina I, A multi-agent system to construct production orders by employing an expert system and a neural network, Expert Systems with Applications, 2009, 36(2): 2937–2946.

    Article  Google Scholar 

  32. Han G S, Guan Z H, Chen J, et al., Multi-tracking of first order multi-agent networks via self-triggered control, Asian Journal of Control, 2015, 17(4): 1320–1329.

    Article  MathSciNet  MATH  Google Scholar 

  33. Han G S, Guan Z H, Li J, et al., Multi-tracking of second-order multi-agent systems using impulsive control, Nonlinear Dynamics, 2016, 84(3): 1771–1781.

    Article  MathSciNet  MATH  Google Scholar 

  34. Jia Q, Han Z, and Tang W, Synchronization of multi-agent systems with time-varying control and delayed communications, IEEE Transactions on Circuits and Systems I: Regular Papers, 2019, 66(11): 4429–4438.

    Article  MathSciNet  MATH  Google Scholar 

  35. Nagy M, Akos Z, Biro D, et al., Hierarchical group dynamics in pigeon flocks, Nature, 2010, 464(7290): 890–893.

    Article  Google Scholar 

  36. Shang Y L, Fixed-time group consensus for multi-agent systems with non-linear dynamics and uncertainties, IET Control Theory and Applications, 2018, 12(3): 395–404.

    Article  MathSciNet  Google Scholar 

  37. Hu J, Wang Z, Liu G P, et al., A prediction-based approach to distributed filtering with missing measurements and communication delays through sensor networks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(11): 7063–7074.

    Article  Google Scholar 

  38. Liu G P, Coordinated control of networked multiagent systems with communication constraints using a proportional integral predictive control strategy, IEEE Transactions on Cybernetics, 2020, 50(11): 4735–4743.

    Article  Google Scholar 

  39. Hu J, Zhang H, Yu X, et al., Design of sliding-mode-based control for nonlinear systems with mixed-delays and packet losses under uncertain missing probability, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(5): 3217–3228.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Harbin University of Science and Technology, Harbin, 150080, China

    Yanjiang Li, Chong Tan, Jingxian Wu & Yin Cui

  2. Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen, 518055, China

    Guo-Ping Liu

Authors
  1. Yanjiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chong Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingxian Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guo-Ping Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yin Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chong Tan.

Ethics declarations

LIU Guoping is an editorial board member for Journal of Systems Science & Complexity and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Additional information

This work was supported by Natural Science Foundation of Heilongjiang Province of China under Grant No. LH2022F033, the National Natural Science Foundation of China under Grant Nos. 61903104, 61773144 and 12071102, and also Heilongjiang Postdoctoral Scientific Research Developmental Fund under Grant Nos. LBH-Q20099 and LBH-Q20168.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Tan, C., Wu, J. et al. Stability Analysis and Group Consensus Tracking Predictive Control of Multi-Agent Systems. J Syst Sci Complex 36, 1851–1877 (2023). https://doi.org/10.1007/s11424-023-1397-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-023-1397-4

Keywords

Search

Navigation