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Stochastic Consensus for Heterogeneous Multi-agent Networks With Constraints and Communication Noises

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  • Control Theory and Applications
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Abstract

The mean-square consensus of the discrete-time heterogeneous multi-agent systems (HMASs) with convex position constraints, nonconvex velocity constraints and communication noises is reported in this paper, where the dynamics of HMASs are composed of first-order or second-order difference equations, and the noises are assumed to be martingale difference sequences. Firstly, a new algorithm is designed based on the information from neighbor agents with noises, and the original system is changed into an equivalent one by introducing a coordinate transformation. Secondly, when the communication graph is joint strongly connected, it is proved that mean-square consensus can be achieved by the properties of stochastic matrix, projection operator and martingale, and the position and velocity states of agents stay at the corresponding constraint sets. Specially, the situations of a network containing only first-order agents or second-order agents are considered, respectively. Finally, the correctness of the theoretical results is verified by numerical simulations.

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References

  1. R. Rajasekar and P. Prakasam, “Proposed coordinating multiple sampling tasks in sensor field using geometric progression algorithm for efficient data collection in wireless sensor networks,” Wireless Personal Communications, vol. 82, no. 3, pp. 1809–1824, 2015.

    Article  Google Scholar 

  2. J. Fax and R. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol 49, no. 9, pp. 1465–1476, 2004.

    Article  MathSciNet  Google Scholar 

  3. M. Campbel, “Collision monitoring within satellite clusters,” IEEE Transactions on Control Systems Technology, vol. 13, no. 1, pp. 42–55, 2005.

    Article  Google Scholar 

  4. R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004.

    Article  MathSciNet  Google Scholar 

  5. A. Nedic, A. Ozdaglar, and P. A. Parrilo, “Constrained consensus and optimization in multi-agent networks,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 922–938, 2010.

    Article  MathSciNet  Google Scholar 

  6. X. Li, Z. Sun, Y. Tang, et al., “Adaptive event-triggered consensus of multiagent systems on directed graphs,” IEEE Transactions on Automatic Control, vol. 66, no. 4, pp. 1670–1685, 2021.

    Article  MathSciNet  Google Scholar 

  7. H. Wang, W. Ren, W, Yu, et al., “Fully distributed consensus control for a class of disturbed second-order multiagent systems with directed networks,” Automatica, 2021.

  8. P. Lin, W. Ren, and H. Gao, “Distributed velocity-constrained consensus of discrete-time multi-agent systems with nonconvex constraints, switching topologies, and delays,” IEEE Transactions on Automatic Control, vol. 62, no. 11, pp. 5788–5794, 2017.

    Article  MathSciNet  Google Scholar 

  9. Y. Zhang, X. Li, and L. Wang, “Distributed H∞ consensus of heterogeneous multi-agent systems with nonconvex constraints’, ISA Transactions, 2022.

  10. M. Lu, J. Wu, X. Zhan, et al., “Consensus of second-order heterogeneous multi-agent systems with and without input saturation,” ISA Transactions, vol. 126, 14–20, 2022.

    Article  Google Scholar 

  11. X. Li, C. Li, Y. Yang, et al., “Consensus for heterogeneous multi-agent systems with nonconvex input constraints and nonuniform time delays,” Journal of the Franklin Institute, vol. 357, no. 6, pp. 3622–3635, 2020.

    Article  MathSciNet  Google Scholar 

  12. P. Liu, F. Xiao, B. Wei, et al., “Distributed constrained optimization problem of heterogeneous linear multi-agent systems with communication delays,” Systems & Control Letters, vol. 155, 2021.

  13. X. Li, C. Li, and Y. Yang, “Heterogeneous linear multiagent consensus with nonconvex input constraints and switching graphs,” Information Sciences, vol. 501, pp. 397–405, 2019.

    Article  MathSciNet  Google Scholar 

  14. L. Mo, S. Guo, and Y. Yu, “Mean-square consensus of heterogeneous multi-agent systems with nonconvex constraints, Markovian switching topologies and delays,” Neurocomputing, vol. 291, pp. 167–174, 2018.

    Article  Google Scholar 

  15. X. Li, Z. Yu, Z. Li, et al., “Group consensus via pinning control for a class of heterogeneous multi-agent systems with input constraints,” Information Sciences, vol. 542, pp. 247–262, 2021.

    Article  MathSciNet  Google Scholar 

  16. L. Mo, Y. Yu, G. Ren, et al., “Constrained consensus of continuous-time heterogeneous multi-agent networks with nonconvex constraints and delays,” Journal of Systems Science and Complexity, vol. 35, pp. 105–122, 2022.

    Article  MathSciNet  Google Scholar 

  17. J. Huang, L. Chen, X. Xie, et al., “Distributed event-triggered consensus control for heterogeneous multi-agent systems under fixed and switching topologies,” International Journal of Control, Automation, and Systems, vol. 17, no. 8, pp. 1946–1956, 2019.

    Article  Google Scholar 

  18. J. Zhang, D. Ding, L. Qing, et al., “Event-triggered control for heterogeneous discrete-time multi-agent systems subject to uncertainties and noises,” International Journal of Control, Automation, and Systems, vol. 18, no. 3, pp. 661–671, 2020.

    Article  Google Scholar 

  19. J. Long, W. Wang, G. Wen, et al., “Output feedback based adaptive consensus tracking for uncertain heterogeneous multi-agent systems with event-triggered communication,” Automatica, vol. 136, 110049, 2022.

    Article  MathSciNet  Google Scholar 

  20. C. Sun, M. Ye, and G. Hu, “Distributed optimization for two types of heterogeneous multiagent systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 3, pp. 1314–1324, 2021.

    Article  MathSciNet  Google Scholar 

  21. Z. Gao, H. Zhang, Y. Cai, et al., “Finite-time event-triggered output consensus of heterogeneous fractional-order multiagent systems with intermittent communication,” IEEE Transactions on Cybernetics, 2021.

  22. L. He and W. Dong, “Distributed adaptive consensus tracking control for heterogeneous nonlinear multi-agent systems,” ISA Transactions, 2022.

  23. H. Du, G. Wen, D. Wu, et al., “Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems,” Automatica, vol. 103, 108797, 2022.

    Google Scholar 

  24. L. Mo and H. Zhang, “Constrained consensus of heterogeneous networks with nonuniform constraints and nonuniform communication delays,” Control Theory & Applications, vol. 40, 2023.

  25. T. Li and J. Zhang, “Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions,” Automatica, vol. 45, no. 8, pp. 1929–1936, 2009.

    Article  MathSciNet  Google Scholar 

  26. T. Li and J. Zhang, “consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises,” IEEE Transactions on Automatic Control, vol. 55, no. 9, pp. 2043–2057, 2010.

    Article  MathSciNet  Google Scholar 

  27. S. S. Ram, A. Nedic, and V. V Veeravalli, “Distributed stochastic subgradient projection algorithms for convex optimization,” Journal of Optimization Theory and Application, vol. 147, no. 3, pp. 516–545, 2010.

    Article  MathSciNet  Google Scholar 

  28. S. Guo, L. Mo, and Y. Yu, “Mean-square consensus of heterogeneous multi-agent systems with communication noises,” Journal of the Franklin Institute, vol. 355, no. 8, pp. 3717–3736, 2018.

    Article  MathSciNet  Google Scholar 

  29. F. Sun, C. Lei, and J. Kurths, “Consensus of heterogeneous discrete-time multi-agent systems with noise over Markov switching topologies,” International Journal of Robust and Nonlinear Control, vol. 31, no. 5, pp. 1530–1541, 2021.

    Article  MathSciNet  Google Scholar 

  30. H. Chen, Stochastic Approximation and its Application, Springer-Verlag New York Inc. 2002.

  31. P. Lin, W. Ren, and Y. Song, “Distributed multi-agent optimization subject to nonidentical constraints and communication delays,” Automatica, vol. 65, pp. 120–131, 2016.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, China

    Haokun Hu

  2. School of Mathematics and Statistic, Centraol South University, Changsha, China

    Haokun Hu

  3. School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing, China

    Lipo Mo

  4. Research Centre for Agri-Product Quality Traceability, Beijing Technology and Business University, Beijing, China

    Lipo Mo

  5. School of Artificial Intelligence and Electrical Engineering, Guizhou Institute of Technology, Guiyang, China

    Fei Long

Authors
  1. Haokun Hu
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  2. Lipo Mo
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  3. Fei Long
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Corresponding author

Correspondence to Lipo Mo.

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All authors declare that no conflict of interest exists.

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This work was supported in part by the National Natural Science Foundation of China under Grant 61973329 and the National Key Technology R&D Program of China under Grant 2021YFD2100605.

Haokun Hu received his M.S. degree from the School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, China, in 2022. He is currently pursuing a Ph.D. degree from the School of Mathematics and Statistics from Central South University, Changsha, China. His research interests include multi-agent systems, stochastic system, machine learning, and distributed control.

Lipo Mo received his B.S. degree in mathematics and applied mathematics from Shihezi university, Shihezi, China, in 2003, and a Ph.D. degree in control theory from the School of Mathematics and Systems Science, Beihang University, Beijing, China, in 2010. He is currently a Professor with the School of E-Business and Logistics, Beijing Technology and Business University, and the School of Mathematics and Statistics, Beijing Technology and Business University, Beijing. His research interests include systems engineering, distributed control and optimization, big data and applied statistics, and supply chain management.

Fei Long received his M.S. degree from the Department of Mathematics, Guizhou University, China, in 2001, and a Ph.D. degree from the College of Automation from Southeast University, Nanjing, in 2006. Currently, he is a professor at Guizhou Institute of Technology. His research interests include switched systems and multiagent systems.

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Hu, H., Mo, L. & Long, F. Stochastic Consensus for Heterogeneous Multi-agent Networks With Constraints and Communication Noises. Int. J. Control Autom. Syst. 22, 1150–1162 (2024). https://doi.org/10.1007/s12555-022-1055-y

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  • DOI: https://doi.org/10.1007/s12555-022-1055-y

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