Skip to main content
Log in

Adaptive Event-triggered Cooperative Tracking Control Under Full-state Constraints Based on Nonlinear Time-varying Multi-agent Systems

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

An adaptive dynamic surface control (DSC) scheme using event triggering mechanism and barrier Lyapunov function (BLF) to constraint state variables and solve energy saving issues is proposed for multi-agent systems (MASs). Furthermore, invented a control algorithm that uses the event-triggered mechanism for not only decrease the number of information exchanges between agents significantly but also decreased utilization of electricity and communication expenses in the control process. DSC and full-state constraints are used to solve the “complexity explosion” problem of the traditional back-stepping method. Simulation and semi-physical experimental platforms were constructed to verify the proposed algorithm is valid.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Y. Hong, J. Hu, and L. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, 2006.

    MathSciNet  Google Scholar 

  2. H. Su, X. Wang, and Z. Lin, “Flocking of multi-agents with a virtual leader,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 293–307, 2009.

    MathSciNet  Google Scholar 

  3. Y. Gao, J. Ma, M. Zuo, T. Jiang, and J. Du, “Consensus of discrete-time second-order agents with time-varying topology and time-varying delays,” Journal of the Franklin Institute, vol. 349, no. 8, pp. 2598–2608, 2012.

    MathSciNet  Google Scholar 

  4. P. Lin, K. Qin, H. Zhao, and M. Sun, “A new approach to average consensus problems with multiple time-delays and jointly-connected topologies,” Journal of the Franklin Institute, vol. 349, no. 1, pp. 293–304, 2012.

    MathSciNet  Google Scholar 

  5. H. Li, G. Chen, T. Huang, Z. Dong, W. Zhu, and L. Gao, “Event-triggered distributed average consensus over directed digital networks with limited communication bandwidth,” IEEE Transactions on Cybernetics, vol. 46, no. 12, pp. 3098–3110, 2016.

    PubMed  Google Scholar 

  6. H. Li, G. Chen, T. Huang, and Z. Dong, “High-performance consensus control in networked systems with limited bandwidth communication and time-varying directed topologies,” IEEE Trans Neural Netw Learn Syst, vol. 28, no. 5, pp. 1043–1054, 2016.

    PubMed  Google Scholar 

  7. E. Nuno, R. Ortega, L. Basa nez, and D. Hill, “Synchronization of networks of nonidentical euler-lagrange systems with uncertain parameters and communication delays,” IEEE Transactions on Automatic Control, vol. 56, no. 4, pp. 935–941, 2011.

    MathSciNet  Google Scholar 

  8. J. Mei, W. Ren, J. Chen, and G. Ma, “Distributed adaptive coordination for multiple lagrangian systems under a directed graph without using neighbors velocity information,” Automatica, vol. 49, no. 6, pp. 1723–1731, 2013.

    MathSciNet  Google Scholar 

  9. W. Chen, X. Li, W. Ren, and C. Wen, “Adaptive consensus of multi-agent systems with unknown identical control directions based on a novel nussbaum-type function,” IEEE Transactions on Automatic Control, vol. 59, no. 7, pp. 1887–1892, 2013.

    MathSciNet  Google Scholar 

  10. G. Zhu, H. Li, X. Zhang, C. Wang, C.-Y. Su, and J. Hu, “Adaptive consensus quantized control for a class of highorder nonlinear multi-agent systems with input hysteresis and full state constraints,” IEEE/CAA Journal of Automatica Sinica, vol. 9, no. 9, pp. 1574–1589, 2022.

    Google Scholar 

  11. X. Zhang, Y. Wang, C. Wang, C.-Y. Su, Z. Li, and X. Chen, “Adaptive estimated inverse output-feedback quantized control for piezoelectric positioning stage,” IEEE Transactions on Cybernetics, vol. 49, no. 6, pp. 2106–2118, 2018.

    PubMed  Google Scholar 

  12. X. Zhang, B. Li, X. Chen, Z. Li, Y. Peng, and C.-Y. Su, “Adaptive implicit inverse control for a class of discrete-time hysteretic nonlinear systems and its application,” IEEE/ASME Transactions on Mechatronics, vol. 25, no. 4, pp. 2112–2122, 2020.

    Google Scholar 

  13. X. Zhang, Y. Wang, G. Zhu, X. Chen, Z. Li, C. Wang, and C.-Y. Su, “Compound adaptive fuzzy quantized control for quadrotor and its experimental verification,” IEEE transactions on cybernetics, vol. 51, no. 3, pp. 1121–1133, 2020.

    Google Scholar 

  14. X. Zhang, Y. Wang, G. Zhu, X. Chen, and C.-Y. Su, “Discrete-time adaptive neural tracking control and its experiments for quadrotor unmanned aerial vehicle systems,” IEEE/ASME Transactions on Mechatronics, 2021.

  15. A. Das and F. L. Lewis, “Distributed adaptive control for synchronization of unknown nonlinear networked systems,” Automatica, vol. 46, no. 12, pp. 2014–2021, 2010.

    MathSciNet  Google Scholar 

  16. A. Das and F. L. Lewis, “Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities,” International Journal of Robust and Nonlinear Control, vol. 21, no. 13, pp. 1509–1524, 2011.

    MathSciNet  Google Scholar 

  17. H. Zhang and F. L. Lewis, “Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics,” Automatica, vol. 48, no. 7, pp. 1432–1439, 2012.

    MathSciNet  Google Scholar 

  18. S. El-Ferik, A. Qureshi, and F. L. Lewis, “Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems,” Automatica, vol. 50, no. 3, pp. 798–808, 2014.

    MathSciNet  Google Scholar 

  19. W. Bai, P. X. Liu, and H. Wang, “Neural-network-based adaptive fixed-time control for nonlinear multiagent nonaffine systems,” IEEE Transactions on Neural Networks and Learning Systems, 2022.

  20. W. Bai, P. Xiaoping Liu, H. Wang, and M. Chen, “Adaptive finite-time control for nonlinear multi-agent high-order systems with actuator faults,” International Journal of Systems Science, pp. 1–24, 2022.

  21. W. Wang, J. Huang, C. Wen, and H. Fan, “Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots,” Automatica, vol. 50, no. 4, pp. 1254–1263, 2014.

    MathSciNet  Google Scholar 

  22. J. Peng and X. Ye, “Distributed adaptive controller for the output-synchronization of networked systems in semistrict feedback form,” Journal of the Franklin Institute, vol. 351, no. 1, pp. 412–428, 2014.

    MathSciNet  Google Scholar 

  23. M. Krstic, P. V. Kokotovic, and I. Kanellakopoulos, Nonlinear and Adaptive Control Design, John Wiley & Sons, Inc., 1995.

  24. S. J. Yoo, “Distributed adaptive containment control of uncertain nonlinear multi-agent systems in strict-feedback form,” Automatica, vol. 49, no. 7, pp. 2145–2153, 2013.

    MathSciNet  Google Scholar 

  25. D. Swaroop, J. K. Hedrick, P. P. Yip, and J. C. Gerdes, “Dynamic surface control for a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1893–1899, 2000.

    MathSciNet  Google Scholar 

  26. S. J. Yoo, J. B. Park, and Y. H. Choi, “Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs,” Automatica, vol. 45, no. 2, pp. 436–443, 2009.

    MathSciNet  Google Scholar 

  27. W. Chenliang and L. Yan, “Adaptive dynamic surface control for linear multivariable systems,” Automatica, vol. 46, no. 10, pp. 1703–1711, 2010.

    MathSciNet  Google Scholar 

  28. L. Nie, Y. Luo, W. Gao, and M. Zhou, “Rate-dependent asymmetric hysteresis modeling and robust adaptive trajectory tracking for piezoelectric micropositioning stages,” Nonlinear Dynamics, vol. 108, no. 3, pp. 2023–2043, 2022.

    Google Scholar 

  29. C. Wang and L. Guo, “Adaptive cooperative tracking control for a class of nonlinear time-varying multi-agent systems,” Journal of the Franklin Institute, vol. 354, no. 15, pp. 6766–6782, 2017.

    MathSciNet  Google Scholar 

  30. G. Guo, L. Ding, and Q.-L. Han, “A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems,” Automatica, vol. 50, no. 5, pp. 1489–1496, 2014.

    MathSciNet  Google Scholar 

  31. D. V. Dimarogonas and K. H. Johansson, “Event-triggered control for multi-agent systems,” Proc. of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp. 7131–7136, IEEE, 2009.

  32. D. Li, C. P. Chen, Y.-J. Liu, and S. Tong, “Neural network controller design for a class of nonlinear delayed systems with time-varying full-state constraints,” IEEE transactions on neural networks and learning systems, vol. 30, no. 9, pp. 2625–2636, 2019.

    MathSciNet  PubMed  Google Scholar 

  33. L. Liu, Y.-J. Liu, and S. Tong, “Fuzzy-based multierror constraint control for switched nonlinear systems and its applications,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 8, pp. 1519–1531, 2018.

    Google Scholar 

  34. L. Tang, D. Ma, and J. Zhao, “Adaptive neural control for switched non-linear systems with multiple tracking error constraints,” IET Signal Processing, vol. 13, no. 3, pp. 330–337, 2019.

    Google Scholar 

  35. Y. Zhang, H. Liang, H. Ma, Q. Zhou, and Z. Yu, “Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints,” Applied Mathematics and Computation, vol. 326, pp. 16–32, 2018.

    MathSciNet  Google Scholar 

  36. Y. Liu, H. Zhang, J. Sun, and Y. Wang, “Adaptive fuzzy containment control for multi-agent systems with state constraints using unified transformation functions,” IEEE Transactions on Fuzzy Systems, 2020.

  37. J. Lian, Y. Meng, and L.-l. Li, “Formation control and obstacle avoidance for multi-agent systems using barrier lyapunov functions,” Proc. of Eighth International Conference on Information Science and Technology (ICIST), pp. 15–20, IEEE, 2018.

  38. J. Zhang, C.-E. Ren, and Q. Fu, “Adaptive event-triggered control for stochastic nonlinear multi-agent systems with unknown control directions,” International Journal of Control, Automation, and Systems, vol. 19, no. 9, pp. 2950–2958, 2021.

    Google Scholar 

  39. G. Zhao, Z. Wang, and X. Fu, “Fully distributed dynamic event-triggered semiglobal consensus of multi-agent uncertain systems with input saturation via low-gain feedback,” International Journal of Control, Automation, and Systems, vol. 19, no. 4, pp. 1451–1460, 2021.

    Google Scholar 

  40. X. Li, D. Ma, X. Hu, and Q. Sun, “Dynamic event-triggered control for heterogeneous leader-following consensus of multi-agent systems based on input-to-state stability,” International Journal of Control, Automation, and Systems, vol. 18, no. 2, pp. 293–302, 2020.

    CAS  Google Scholar 

  41. S. Chen, H. Jiang, and Z. Yu, “Fully distributed event-triggered semi-global consensus of multi-agent systems with input saturation and directed topology,” International Journal of Control, Automation, and Systems, vol. 17, no. 12, pp. 3102–3112, 2019.

    Google Scholar 

  42. L. Jian, J. Hu, J. Wang, K. Shi, Z. Peng, Y. Yang, and J. Huang, “Distributed functional observer-based event-triggered containment control of multi-agent systems,” International Journal of Control, Automation, and Systems, vol. 18, no. 5, pp. 1094–1102, 2020.

    Google Scholar 

  43. C.-E. Ren, Q. Fu, J. Zhang, and J. Zhao, “Adaptive event-triggered control for nonlinear multi-agent systems with unknown control directions and actuator failures,” Journal of Computational and Nonlinear Dynamics, vol. 105, no. 2, pp. 1657–1672, 2021.

    Google Scholar 

  44. S. Yuan, C. Yu, and J. Sun, “Adaptive event-triggered consensus control of linear multi-agent systems with cyber attacks,” Neurocomputing, vol. 442, pp. 1–9, 2021.

    Google Scholar 

  45. F. Yuan, J. Lan, Y. Liu, and L. Liu, “Adaptive nn control for nonlinear multi-agent systems with unknown control direction and full state constraints,” IEEE Access, vol. 9, pp. 24425–24432, 2020.

    Google Scholar 

  46. D. Yao, C. Dou, N. Zhao, and T. Zhang, “Practical fixed-time adaptive consensus control for a class of multi-agent systems with full state constraints and input delay,” Neurocomputing, vol. 446, pp. 156–164, 2021.

    Google Scholar 

  47. L. Shang and M. Cai, “Adaptive practical fast finite-time consensus protocols for high-order nonlinear multi-agent systems with full state constraints,” IEEE Access, 2021.

  48. T. Han, Z.-H. Guan, B. Xiao, and H. Yan, “Bipartite average tracking for multi-agent systems with disturbances: finite-time and fixed-time convergence,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 68, no. 10, pp. 4393–4402, 2021.

    Google Scholar 

  49. X. Li, Y. Tang, and H. R. Karimi, “Consensus of multiagent systems via fully distributed event-triggered control,” Automatica, vol. 116, p. 108898, 2020.

    MathSciNet  Google Scholar 

  50. C. Deng, C. Wen, J. Huang, X.-M. Zhang, and Y. Zou, “Distributed observer-based cooperative control approach for uncertain nonlinear mass under event-triggered communication,” IEEE Transactions on Automatic Control, vol. 67, no. 5, pp. 2669–2676, 2021.

    MathSciNet  Google Scholar 

  51. T. Han and W. X. Zheng, “Bipartite output consensus for heterogeneous multi-agent systems via output regulation approach,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 1, pp. 281–285, 2020.

    ADS  Google Scholar 

  52. L. Hao, X. Zhan, J. Wu, T. Han, and H. Yan, “Bipartite finite time and fixed time output consensus of heterogeneous multiagent systems under state feedback control,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 6, pp. 2067–2071, 2020.

    ADS  Google Scholar 

  53. T. Liu and Z.-P. Jiang, “Event-based control of nonlinear systems with partial state and output feedback,” Automatica, vol. 53, pp. 10–22, 2015.

    MathSciNet  Google Scholar 

  54. K. Kogiso and K. Hirata, “Reference governor for constrained systems with time-varying references,” Proc. of IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, pp. 359–364, IEEE, 2006.

  55. D. Limón, I. Alvarado, T. Alamo, and E. F. Camacho, “Mpc for tracking piecewise constant references for constrained linear systems,” Automatica, vol. 44, no. 9, pp. 2382–2387, 2008.

    MathSciNet  Google Scholar 

  56. C. Wang, C. Wen, and Y. Lin, “Decentralized adaptive backstepping control for a class of interconnected nonlinear systems with unknown actuator failures,” Journal of the Franklin Institute, vol. 352, no. 3, pp. 835–850, 2015.

    MathSciNet  Google Scholar 

  57. M. M. Polycarpou and P. A. Ioannou, “A robust adaptive nonlinear control design,” Proc. of American Control Conference, pp. 1365–1369. IEEE, 1993.

  58. A. Theodorakopoulos and G. A. Rovithakis, “Guaranteeing preselected tracking quality for uncertain strict-feedback systems with deadzone input nonlinearity and disturbances via low-complexity control,” Automatica, vol. 54, pp. 135–145, 2015.

    MathSciNet  Google Scholar 

  59. K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, 2009.

    MathSciNet  Google Scholar 

  60. W. Wang, J. Liang, C. Pan, Y. Cai, and L. Chen, “NLS based hierarchical anti-disturbance controller for vehicle platoons with time-varying parameter uncertainties,” IEEE Transactions on Intelligent Transportation Systems, 2022.

  61. L. Xing, C. Wen, Z. Liu, H. Su, and J. Cai, “Event-triggered adaptive control for a class of uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 2071–2076, 2016.

    MathSciNet  Google Scholar 

  62. P. Shi, H. Wang, and C.-C. Lim, “Network-based event-triggered control for singular systems with quantizations,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1230–1238, 2015.

    Google Scholar 

  63. A. Girard, “Dynamic triggering mechanisms for event-triggered control,” IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1992–1997, 2014.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Xiuyu Zhang or Guoqiang Zhu.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported by the Jilin Scientific and Technological Development Program under grand 20210509053RQ.

Lingfang Sun was born in Heze City, China. He received his B.S. and M.S. degrees from Northeast Electric Power University, Jilin, China, in 1993 and 1999, respectively, and a Ph.D. degree from North China Electric Power University, Beijing, China, in 2004. He is currently a Professor with the School of Automation Engineering, Northeast Electric Power University, Jilin, China. His research interests include advanced control of thermal process and fouling monitoring of heat exchange equipment.

Yida Zang received his B.S. degree in transmission engineering from Northeast Electric Power University in 2018. Currently, he is studying for a master’s degree in control science and engineering at Northeastern Electric Power University. His research interests include nonlinear control, adaptive control, and multi-agent systems.

Xiuyu Zhang was born in Jilin City, China. He received his B.S. and M.S. degrees from Northeast Electric Power University, Jilin, China, in 2003 and 2006, respectively, and a Ph.D. degree from Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 2012. He is currently a Professor with the School of Automation Engineering, Northeast Electric Power University, Jilin, China. His research interests include robust and adaptive control for nonlinear systems with smart-material based actuators.

Guoqiang Zhu was born in Heze City, China. He received his B.S. and M.S. degrees from Northeast Electric Power University, Jilin, China, in 2003 and 2006, respectively, and a Ph.D. degree from Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 2015. He is currently an Associated Professor with the School of Automation Engineering, Northeast Electric Power University, and also a Member of Jilin Provincial International Joint Research Center of Precision Drive and Intelligent Control. His research interests include robust and adaptive control for nonlinear systems.

Cheng Zhong was born in Changchun City, China. He received his B.S. and M.S. degrees from Northeast Electric Power University, Jilin, China, in 2003 and 2006, respectively. He is currently a senior engineer of Tangshan Power Supply Company, State Grid Jibei Electric Power Company, Tangshan. China. His research interests include power system stability analysis and power supply management.

Chenliang Wang received his B.Eng. degree in automation and a Ph.D. degree in control theory and control engineering from the School of Automation Science and Electrical Engineering, Beihang University, in 2008 and 2013, respectively. Currently, he is an Associate Professor with the School of Automation Science and Electrical Engineering, Beihang University. From April 2015 to April 2016, he was a Visiting Scholar at National University of Singapore, Singapore. His research interests include anti-disturbance control, adaptive control, and their applications to flight vehicles.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, L., Zang, Y., Zhang, X. et al. Adaptive Event-triggered Cooperative Tracking Control Under Full-state Constraints Based on Nonlinear Time-varying Multi-agent Systems. Int. J. Control Autom. Syst. 22, 867–882 (2024). https://doi.org/10.1007/s12555-022-0435-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-022-0435-7

Keywords

Navigation