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Distributed Cooperative Control of Singular Multi-agent Systems Based on Fuzzy Logic Approach

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Abstract

This paper studies the consensus issue of nonlinear singular multi-agent systems under undirected graphs based on fuzzy logic systems. The main objective is to develop a novel collaborative control algorithm to achieve consensus and impulse free for each agent described by nonlinear singular systems while only knowing local information, namely the state information of the agent itself and its neighbors. To overcome the analysis limitation of nonlinear singular multi-agent systems, the fuzzy logic system method is applied to deal with nonlinear items. Specifically, the consensus issue of singular multi-agent systems with fuzzy logic systems is equivalently simplified to an asymptotic stability analysis process for error systems. To achieve this objective, a novel distributed adaptive collaborative controller is designed, where the adaptive rate adjusts the coupling weight between each agent. In the research of the singular linear multi-agent system, a tolerance region is introduced, and stability of the closed-loop system is established according to Lyapunov theory. Then, fuzzy approximation theory is used to transform unknown nonlinear functions into fuzzy functions satisfying Lipschitz conditions, and the stability and impulse-free property are addressed by constructing LMI conditions. Finally, the effectiveness of the presented approach is demonstrated through two numerical examples.

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References

  1. Jin, Z.H., Ahn, C.K., Li, J.W.: Momentum-based distributed continuous-time nonconvex optimization of nonlinear multi-agent systems via timescale separation. IEEE Trans. Netw. Sci. Eng. 10(2), 980–989 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  2. Jin, Z.H., Qin, Z.Y., Zhang, X.F., Guan, C.: A leader-following consensus problem via a distributed observer and fuzzy input-to-output small-gain theorem. IEEE Trans. Control Netw. Syst. 9(1), 62–74 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  3. Rao, S., Ghose, D.: Sliding mode control-based autopilots for leaderless consensus of unmanned aerial vehicles. IEEE Trans. Control Syst. Technol. 22(5), 1964–1972 (2014)

    Article  MATH  Google Scholar 

  4. Tsai, C.-C., Hsu, C.-F., Wu, C.-W., Tai, F.-C.: Cooperative localization using fuzzy DDEIF and broad learning system for uncertain heterogeneous omnidirectional multi-robots. Int. J. Fuzzy Syst. 21, 2542–2555 (2019)

    Article  MATH  Google Scholar 

  5. Ning, B., Han, Q.L., Lu, Q.: Fixed-time leader-following consensus for multiple wheeled mobile robots. IEEE Trans. Cybern. 50(10), 4381–4392 (2020)

    Article  MATH  Google Scholar 

  6. Lu, P.F., Yu, W.W., Chen, G.R., Yu, X.H.: Leaderless consensus of ring-networked mobile robots via distributed saturated control. IEEE Trans. Ind. Electron. 67(12), 10723–10731 (2020)

    Article  MATH  Google Scholar 

  7. Jin, Z.H., Bai, L.S., Wang, Z.X., Zhang, P.P.: Self-triggered distributed formation control of fixed-wing unmanned aerial vehicles subject to velocity and overload constraints. IEEE Trans. Autom. Sci. Eng. (2023). https://doi.org/10.1109/TASE.2023.3292176

    Article  MATH  Google Scholar 

  8. Kuo, C.W., Kazerooni, C., Tsai, C., Lee, C.T.: Intelligent leader-following consensus formation control using recurrent neural networks for small-size unmanned helicopters. IEEE Trans. Syst. Man Cybern. Syst. 51(2), 1288–1301 (2021)

    Article  Google Scholar 

  9. Wang, D., Zong, Q., Tian, B., Shao, S., Zhan, X., Zhao, X.: Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters. ISA Trans. 73, 208–226 (2018)

    Article  MATH  Google Scholar 

  10. Mustafa, A., Modares, H.: Attack analysis and resilient control design for discrete-time distributed multi-agent systems. IEEE Robot. Autom. Lett. 5(2), 369–376 (2020)

    Article  MATH  Google Scholar 

  11. Qu, X., Liang, X., Hou, Y.: Fuzzy state observer-based cooperative path-following control of autonomous underwater vehicles with unknown dynamics and ocean disturbances. Int. J. Fuzzy Syst. 23, 1849–1859 (2021)

    Article  MATH  Google Scholar 

  12. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Olfati-Saber, R., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ren, W., Beard, R.W.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)

    Article  MATH  Google Scholar 

  15. Nedic, A., Ozdaglar, A., Parrilo, P.A.: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Autom. Control 55(4), 922–938 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Qin, J.H., Yu, C.B., Gao, H.J.: Coordination for linear multiagent systems with dynamic interaction topology in the leader-following framework. IEEE Trans. Ind. Electron. 61(5), 2412–2422 (2014)

    Article  MATH  Google Scholar 

  17. Xing, S.Y., Zheng, W.X., Deng, F.Q., Chang, C.: An enhanced input-delay approach to sampled-data stabilization for nonlinear stochastic singular systems based on T-S fuzzy models. IEEE Trans. Fuzzy Syst. 30(8), 2943–2956 (2022)

    Article  MATH  Google Scholar 

  18. Tognetti, E.S., Calliero, T.R., Morǎrescu, I., Daafouz, J.: Synchronization via output feedback for multi-agent singularly perturbed systems with guaranteed cost. Automatica 128, 109549 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, S., Huang, J.: Cooperative output regulation of singular multi-agent systems under switching network by standard reduction. IEEE Trans. Circuits Syst. I Regul. Pap. 65(4), 1377–1385 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang, X.R., Liu, G.P.: Necessary and sufficient consensus conditions of descriptor multi-agent systems. IEEE Trans. Circuits Syst. I Regul. Pap. 59(11), 2669–2677 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Xi, J., Yu, Y., Liu, G., Zhong, Y.: Guaranteed-cost consensus for singular multi-agent systems with switching topologies. IEEE Trans. Circuits Syst. I Regul. Pap. 61(5), 1531–1542 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu, X.F., Xie, Y.F., Li, F.B., Gui, W.H.: Admissible consensus for homogenous descriptor multiagent systems. IEEE Trans. Syst. Man Cybern. Syst. 51(2), 965–974 (2021)

    Article  MATH  Google Scholar 

  23. Wang, H., Yu, W.W., Wen, G.H., Chen, G.R.: Fixed-time consensus of nonlinear multi-agent systems with general directed topologies. IEEE Trans. Circuits Syst. II Express Briefs 66(9), 1587–1591 (2019)

    MATH  Google Scholar 

  24. Xian, C.X., Zhao, Y., Wu, Z.G., Wen, G.H., Pan, J.A.: Event-triggered distributed average tracking control for Lipschitz-type nonlinear multiagent systems. IEEE Trans. Cybern. 53(2), 779–792 (2023)

    Article  MATH  Google Scholar 

  25. Zheng, T., He, M., Xi, J.X., Liu, G.B.: Leader-following guaranteed-performance consensus design for singular multi-agent systems with Lipschitz nonlinear dynamics. Neurocomputing 266, 651–658 (2017)

    Article  MATH  Google Scholar 

  26. Yuan, X., Chen, B., Lin, C.: Prescribed finite-time adaptive fuzzy control via output feedback for output-constrained nonlinear systems. Int. J. Fuzzy Syst. 25, 1055–1068 (2023)

    Article  MATH  Google Scholar 

  27. Li, B.M., Xia, J.W., Zhang, H.S., Shen, H., Wang, Z.: Event-triggered adaptive fuzzy tracking control for nonlinear systems. Int. J. Fuzzy Syst. 22, 1389–1399 (2020)

    Article  MATH  Google Scholar 

  28. Jin, Z.H., Sun, X.J., Qin, Z.Y., Ahn, C.K.: Fuzzy small-gain approach for the distributed optimization of T-S fuzzy cyber-physical systems. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2022.3202576

    Article  MATH  Google Scholar 

  29. Jin, Z.H., Li, J.W., Wang, Z.X.: Input-to-state stability of the nonlinear fuzzy systems via small-gain theorem and decentralized sliding mode control. IEEE Trans. Fuzzy Syst. 30(8), 2993–3008 (2022)

    Article  MATH  Google Scholar 

  30. Chen, S., Ho, D.W., Li, L., Liu, M.: Fault-tolerant consensus of multi-agent system with distributed adaptive protocol. IEEE Trans. Cybern. 45(10), 2142–2155 (2014)

    Article  MATH  Google Scholar 

  31. Li, Z., Ren, W., Liu, X., Xie, L.: Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica 49(7), 1986–1995 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Dai, L.: Singular Control Systems. Springer, Berlin (1989)

    Book  MATH  Google Scholar 

  33. Petersen, R., Hollot, V.: A Riccati equation approach to the stabilization of uncertain linear systems. Automatica 22(4), 397–411 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  34. Yang, D., Zhang, Q., Yao, B.: Singular System. Science Press, Beijing (2004)

    MATH  Google Scholar 

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Acknowledgements

This study is completed with funding from the National Natural Science Foundation of China under Grant 62103289. Thanks to Professor Yingying Wang for her guidance and help.

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Authors and Affiliations

  1. The School of Science, Shenyang University of Technology, Shenyang, 110870, Liaoning, China

    Jiawen Li & Yi Zhang

  2. The State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, Liaoning, China

    Zhenghong Jin

  3. The School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Zhenghong Jin

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  1. Jiawen Li
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Correspondence to Yi Zhang or Zhenghong Jin.

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Li, J., Zhang, Y. & Jin, Z. Distributed Cooperative Control of Singular Multi-agent Systems Based on Fuzzy Logic Approach. Int. J. Fuzzy Syst. 26, 390–401 (2024). https://doi.org/10.1007/s40815-023-01607-w

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  • DOI: https://doi.org/10.1007/s40815-023-01607-w

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