International Journal of Fuzzy Systems

, Volume 20, Issue 8, pp 2605–2619 | Cite as

Distributed Adaptive Iterative Learning Consensus for Uncertain Topological Multi-agent Systems Based on T–S Fuzzy Models

  • Hui Wu
  • Junmin LiEmail author
  • Jiaxi Chen


This paper addresses the exactly consensus problem for the multi-agent system with uncertain topology structure. A T–S fuzzy model is presented to describe the uncertain topology structure of multi-agent systems. Under the assumptions that the dynamic of the leader is only available to a portion of the follower agents and there exist initial-state errors in the procedure of the iterative learning, a new distributed adaptive iterative learning control with the distributed initial-state learning is proposed to ensure all the follower agents track the leader on the finite-time interval. Sufficient conditions are obtained by appropriately constructing Lyapunov function for the exactly consensus problem. Furthermore, the approach is also extended to the exactly formation control problem. Finally, the simulation examples are given to verify the efficacy of the theoretical analysis.


Multi-agent system Adaptive iterative learning control T–S fuzzy model Uncertain topology structure 



This work is supported by National Nature Science Foundation of China under Grant 61573013 and by Ph.D. Programs Foundation of Ministry of Education of China under Grant 20130203110021.


  1. 1.
    Ren, W.: Consensus strategies for cooperative control of vehicle formations. IET Control Theory Appl. 1(2), 505–512 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Qu, Z.: Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Springer, London (2009)zbMATHGoogle Scholar
  3. 3.
    Chen, J., Cao, X., Cheng, P., Xiao, Y., Sun, Y.: Distributed collaborative control for industrial automation with wireless sensor and actuator networks. IEEE Trans. Ind. Electron. 57(12), 4219–4230 (2010)CrossRefGoogle Scholar
  4. 4.
    Han, H., Su, C.Y., Stepanenko, Y.: Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators. IEEE Trans. Fuzzy Syst. 9, 315–323 (2001)CrossRefGoogle Scholar
  5. 5.
    Wang, L., Feng, W.J., Chen, M.Z.Q., Wang, Q.Z.: Consensus of nonlinear multi-agent systems with adaptive protocols. Control Theory Appl. IET 8(18), 2245–2252 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Meng, D., Jia, Y.: Formation control for multi-agent systems through an iterative learning design approach. Int. J. Robust Nonlinear Control 24(2), 340–361 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Shi, J., He, X., Wang, Z., et al.: Consensus control for a class of second-order multi-agent systems: an iterative learning approach. In: International Conference on Unmanned Aircraft Systems. IEEE, pp. 841–849 (2013)Google Scholar
  8. 8.
    Chen, F., Chen, Z., Xiang, L., Liu, Z., Yuan, Z.: Reaching a consensus via pinning control. Automatica 45(5), 1215–1220 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Trentelman, H.L., Takaba, K., Monshizadeh, N.: Robust synchronization of uncertain linear multi-agent systems. IEEE Trans. Autom. Control 58(6), 1511–1523 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chen, H.S., Chen, Y.Q.: Iterative learning control for multi-agent formation. In: ICROS-SICE International Joint Conference. pp. 3111–3116 (2009)Google Scholar
  11. 11.
    Liu, Y., Jia, Y.M.: An iterative learning approach to formation control of multi-agent systems. Syst. Control Lett. 61, 148–154 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Meng, D., Jia, Y.: Iterative learning approaches to design finite time consensus protocols for multiagent systems. Syst. Control Lett. 61(1), 187–194 (2012)CrossRefGoogle Scholar
  13. 13.
    Zhang, H.W., Lewi, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48(7), 1432–1439 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yang, S,. Xu, J.X:. Adaptive iterative learning control for multi-agent systems consensus tracking. In: IEEE International Conference on Systems, Man, and Cybernetics. pp. 2803–2808 (2012)Google Scholar
  15. 15.
    Xu, J.X., Yan, R.: On initial conditions in iterative learning control. IEEE Trans. Autom. Control 50, 1349–1354 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Li, J., Li, J.: Adaptive iterative learning control for consensus of multi-agent systems. IET Control Theory Appl. 7(1), 136–142 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Jin, X.: Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking. Syst. Control Lett. 89(2016), 16–23 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Li, J.M., Li, J.S.: Adaptive fuzzy iterative learning control with initial-state learning for coordination control of leader-following multi-agent systems. Fuzzy Sets Syst. 248, 122–137 (2014)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Samanta, S., Sarkar, B.: Generalized fuzzy trees. Int. J. Comput. Intell. Syst. 10(1), 711–720 (2017)CrossRefGoogle Scholar
  20. 20.
    Samanta, S., Sarkar, B., Shin, D., et al.: Completeness and regularity of generalized fuzzy graphs. Springerplus 5(1), 1979 (2016)CrossRefGoogle Scholar
  21. 21.
    Pramanik, T.: Fuzzy φ-tolerance competition Graphs. Soft. Comput. 21(13), 3723–3734 (2016)CrossRefGoogle Scholar
  22. 22.
    Pramanik, T., Samanta, S., Pal, M., et al.: Interval-valued fuzzy ϕ-tolerance competition graphs. In: European Conference on Logics in Artificial Intelligence. Springer, New York. pp. 62–76 (2016)Google Scholar
  23. 23.
    Sarkar, B., Mahapatra, A.S.: Periodic review fuzzy inventory model with variable lead time and fuzzy demand. Int. Trans. Oper. Res. 24(5), 1197–1227 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)CrossRefGoogle Scholar
  25. 25.
    Xiong, W.J., Yu, W.W., Lv, J.H., Yu, X.H.: Fuzzy modelling and consensus of nonlinear multiagent systems with variable structure. IEEE Trans. Circuits Syst. I Regul. Pap. 61(4), 1183–1191 (2014)CrossRefGoogle Scholar
  26. 26.
    Hong, Y.G., Hu, J.P., Gao, L.X.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42, 1177–1182 (2006)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Sun, M.X.: A Barbalat-like lemma with it application to learning control. IEEE Trans. Autom. Control 54, 2222–2225 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anPeople’s Republic of China

Personalised recommendations