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Finite-Time Consensus of Stochastic Nonlinear Multi-agent Systems

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Abstract

This article studies the finite-time consensus of the stochastic nonlinear multi-agent systems under a directed communication topology. Since the inherent nonlinear dynamics and stochastic disturbances in multi-agent systems are completely unknown, the existing finite-time stability criterion becomes unavailable. To handle this difficulty, by applying the mean value theorem of integrals, a key finite-time stability criterion in integral form is first established. Then, based on the approximation property of the fuzzy logic systems, a distributed adaptive fuzzy control scheme is presented. Under the presented control strategy, the finite-time consensus of the stochastic nonlinear multi-agent systems is achieved. By applying Jessen’s inequality and Theorem 1, the finite-time stability of the closed system is proved. Finally, the simulation result shows the validity of the distributed controller.

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References

  1. Ren, W.: On consensus algorithms for double-integrator dynamics. IEEE Trans. Autom. Control 53(6), 1053–1059 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Su, H., Chen, G., Wang, X., Lin, Z.: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47(2), 368–375 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Su, H., Wang, X., Chen, G.: Rendezvous of multiple mobile agents with preserved network connectivity. Syst. Control Lett. 59(5), 313–322 (2010)

    MathSciNet  MATH  Google Scholar 

  4. Li, H.Y., Chen, Z.R., Wu, L.G.: Event-triggered fault detection of nonlinear networked systems. IEEE Trans. Cybern. 47(4), 1041–1052 (2017)

    Google Scholar 

  5. Li, Z., Ren, W., Liu, X., Fu, M.: Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int. J. Robust. Nonlinear Control 23(5), 534–547 (2013)

    MathSciNet  MATH  Google Scholar 

  6. Das, A., Lewis, F.L.: Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities. Int. J. Robust Nonlinear Control 21(13), 1509–1524 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Chen, W.S., Li, X.B., Jiao, L.C.: Quantized consensus of second-order continuous-time multi-agent systems with a directed topology via sampled data. Automatica 49(1), 2236–2242 (2013)

    MathSciNet  MATH  Google Scholar 

  8. Mei, J., Ren, W., Ma, G.: Distributed containment control for Lagrangian networks with parameteric uncertaities under a directed graph. Automatica 48(4), 653–659 (2012)

    MathSciNet  MATH  Google Scholar 

  9. Zhang, H.W., Lewis, F.L., Qu, Z.: Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs. IEEE Trans. Ind. Electron 59(7), 3026–3041 (2012)

    Google Scholar 

  10. Zhang, H.W., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48(1), 1432–1439 (2012)

    MathSciNet  MATH  Google Scholar 

  11. Xie, Y.J., Lin, Z.L.: Global optimal consensus for higher-order multi-agent systems with bounded controls. Automatica 99, 302–307 (2019)

    MathSciNet  MATH  Google Scholar 

  12. Zhang, Z.H., Wang, C.L., Cai, X.: Consensus control of higher-order nonlinear multi-agent systems with unknown control directions. Neurocomputing 359, 122–129 (2019)

    Google Scholar 

  13. Qu, Z., Li, C., Lewis, F.: Cooperative control with distributed gain adaptation and connectivity estimation for directed networks. Int. J. Robust Nonlinear Control 24(3), 450–476 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Li, H., Gao, Y., Shi, P., Lam, H.K.: Observer-based fault detection for nonlinear systems with sensor fault and limited communication capacity. IEEE Trans. Autom. Control 61(9), 2745–2751 (2016)

    MathSciNet  MATH  Google Scholar 

  15. Li, Y.M., Li, K.W., Tong, S.C.: Adaptive neural network finite-time control for multi-input and multi-output nonlinear systems with the powers of odd rational numbers. IEEE Trans. Neural Netw. Lear. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2933409

    Article  Google Scholar 

  16. Li, Y.M., Li, K.W., Tong, S.C.: Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO non-strict feedback systems. IEEE Trans. Fuzzy Syst. 27(1), 96–110 (2019)

    MathSciNet  Google Scholar 

  17. Lu, K., Liu, Z., Chen, C.L.P., Zhang, Y.: Event-triggered neural control of nonlinear systems with rate-dependent hysteresis input based on a new filter. IEEE Trans. Neural Netw. Lear. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2919641

    Article  Google Scholar 

  18. Wang, F., Liu, Z., Li, X.H., Zhang, Y., Chen, C.L.P.: Observer-based finite time control of nonlinear systems with actuator failures. Inf. Sci. 500, 1–14 (2019)

    MathSciNet  Google Scholar 

  19. Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive quantized controller design via backstepping and stochastic small-gain approach. IEEE Trans. Fuzzy Syst. 24(2), 330–343 (2016)

    Google Scholar 

  20. Yu, J.P., Zhao, L., Yu, H.S., Lin, C.: Barrier Lyapunov functions-based command filtered output feedback control for full-state constrained nonlinear systems. Automatica 105, 71–79 (2019)

    MathSciNet  MATH  Google Scholar 

  21. Wang, H.Q., Liu, P.X.P., Zhao, X.D., Liu, X.P.: Adaptive fuzzy finite-time control of nonlinear systems with actuator faults. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2902868

    Article  Google Scholar 

  22. Lv, W., Wang, F.: Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks. Adv. Differ. Equ. 1, 1 (2017). https://doi.org/10.1186/s13662-017-1426-5

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu, F.: Boundedness and continuity of maximal operators associated to polynomial compound curves on Triebel-Lizorkin spaces. Math. Inequal. Appl. 22(1), 25–44 (2019)

    MathSciNet  MATH  Google Scholar 

  24. Yu, J.P., Shi, P., Zhao, L.: Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica 92, 173–180 (2018)

    MathSciNet  MATH  Google Scholar 

  25. Zhang, L.C., Liang, H.J., Sun, Y.H., Ahn, C.K.: Adaptive event-triggered fault detection for semi-Markovian jump systems with output quantization. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2912846

    Article  Google Scholar 

  26. Li, C.D., Gao, J.L., Yi, J.Q., Zhang, G.Q.: Analysis and design of functionally weighted single-input-rule-modules connected fuzzy inference systems. IEEE Trans. Fuzzy Syst. 26(1), 56–71 (2018)

    Google Scholar 

  27. Chen, B., Zhang, H.G., Liu, X., Lin, C.: Neural observer and adaptive neural control design for a class of nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4261–4271 (2018)

    Google Scholar 

  28. Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive fuzzy control for a class of stochastic pure-feedback nonlinear systems with unknown hysteresis. IEEE Trans. Fuzzy Syst. 24(1), 140–152 (2016)

    Google Scholar 

  29. Chen, B., Liu, X., Lin, C.: Observer and adaptive fuzzy control design for nonlinear strict-feedback systems with unknown virtual control coefficients. IEEE Trans. Fuzzy Syst. 26, 1732–1743 (2018)

    Google Scholar 

  30. Zhao, Z.H., Yu, J.P., Zhao, L., Yu, H.S., Lin, C.: Adaptive fuzzy control for induction motors stochastic nonlinear systems with input saturation based on command filtering. Inf. Sci. 463, 186–195 (2018)

    MathSciNet  Google Scholar 

  31. Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive finite-time control of stochastic nonlinear systems with actuator failures. Fuzzy Sets Syst. 374, 170–183 (2019)

    MathSciNet  MATH  Google Scholar 

  32. Wang, F., Zhang, X.Y., Chen, B.: Adaptive finite-time tracking control of switched nonlinear systems. Inf. Sci. 421, 126–135 (2017)

    MathSciNet  Google Scholar 

  33. Li, X., Zhang, B., Li, P., Zhou, Q., Lu, R.: Finite-horizon H-infinity state estimation for periodic neural networks over fading channels. IEEE Trans. Neural Netw. Lear. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2920368

    Article  Google Scholar 

  34. Wang, F., Zhang, X.Y.: Adaptive finite time control of nonlinear systems under time-varying actuator failures. IEEE Trans. Syst., Man, Cybern., Syst. 49(9), 1845–1852 (2019)

    Google Scholar 

  35. Li, X., Zhou, Q., Li, P., Li, H., Lu, R.: Event-triggered consensus control for multi-agent systems against false data injection attacks. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2937951

    Article  Google Scholar 

  36. Li, C.D., Yi, J.Q., Wang, H.K., Zhang, G.Q., Li, J.Q.: Interval data driven construction of shadowed sets with application to linguistic word modelling. Inf. Sci. (2018). https://doi.org/10.1016/j.ins.2018.11.018

    Article  Google Scholar 

  37. Cao, L., Li, H., Dong, G., Lu, R.: Event-triggered control for multi-agent systems with sensor faults and input saturation. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2938216

    Article  Google Scholar 

  38. Wang, J.M., Cheng, H.D., Meng, X.Z.: Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse. Adv. Differ. Equ. (2017). https://doi.org/10.1186/s13662-017-1300-5

  39. Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive quantized fuzzy control of stochastic nonlinear systems with actuator dead-zone. Inf. Sci. 370–371, 385–401 (2016)

    MATH  Google Scholar 

  40. Li, Y.N., Cheng, H.D.: Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy. Adv. Differ. Equ. (2018). https://doi.org/10.1186/s13662-018-1484-3

    Article  MathSciNet  MATH  Google Scholar 

  41. Lai, G.Y., Liu, Z., Zhang, Y., Chen, C.L.P., Xie, S.L., Liu, Y.J.: Fuzzy adaptive inverse compensation method to tracking control of uncertain nonlinear systems with generalized actuator dead zone. IEEE Trans. Fuzzy Syst. 25(1), 191–204 (2017)

    Google Scholar 

  42. Wang, F., Chen, B., Sun, Y.M., Gao, Y.L., Lin, C.: Finite-time fuzzy control of stochastic nonlinear systems. IEEE Trans. Cybern. 1, 1 (2019). https://doi.org/10.1109/TCYB.2019.2925573

    Article  Google Scholar 

  43. Wang, J.M., Cheng, H.D.: Periodic solution and control optimization of a prey-predator model with two types of harvesting. Adv. Differ. Equ. 1, 1 (2018). https://doi.org/10.1186/s13662-018-1499-9

    Article  MathSciNet  Google Scholar 

  44. Wang, F., Chen, B., Sun, Y.M., Lin, C.: Finite time control of switched stochastic nonlinear systems. Fuzzy Set Syst. 365, 140–152 (2019)

    MathSciNet  MATH  Google Scholar 

  45. Du, P., Liang, H., Zhao, S., Ahn, C.K.: Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2918351

    Article  Google Scholar 

  46. Wang, W., Huang, J.S., Wen, C.Y., Fan, H.J.: Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile roboots. Automatica 40, 1254–1263 (2014)

    MATH  Google Scholar 

  47. Wang, F., Liu, Z., Zhang, Y., Chen, B.: Distributed adaptive coordination control for uncertain nonlinear multi-agent systems with dead-zone input. J. Franklin 353(10), 2270–2289 (2016)

    MathSciNet  MATH  Google Scholar 

  48. Qin, Z.H., He, X.X., Li, G., Wu, Y.M.: Robust adaptive consensus of nonstrict-feedback multi-agent systems with quantized input and unmodeled dynamics. Inf. Sci. 498, 117–134 (2019)

    MathSciNet  Google Scholar 

  49. Shahvali, M., Askari, J.: Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems. Neurocomputing 179, 202–210 (2016)

    MATH  Google Scholar 

  50. Wang, F., Chen, B., Lin, C., Li, X.H.: Distributed adaptive neural control for stochastic nonlinear multi-agent systems. IEEE Trans. Cybern. 47(7), 1795–1803 (2017)

    Google Scholar 

  51. Du, H., He, Y., Cheng, Y.: Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans. Circuits Syst. I. Regul. 61(6), 1778–1788 (2014)

    Google Scholar 

  52. Zhao, L., Hua, C.: Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM. Nonlinear Dynam. 75, 311–318 (2014)

    MathSciNet  MATH  Google Scholar 

  53. Bai, H., Arcak, M., Wen, J.T.: Adaptive motion coordination: using relative velocity feedback to track a reference velocity. Automatica 45, 1020–1025 (2009)

    MathSciNet  MATH  Google Scholar 

  54. Yu, H., Xia, X.: Adaptive consensus of multi-agents in networks with jointly connected topologies. Automatica 48(8), 1783–1790 (2012)

    MathSciNet  MATH  Google Scholar 

  55. Hou, Z., Cheng, L., Tan, M.: Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans. Syst. Man, Cybern. 39(3), 636–647 (2009)

    Google Scholar 

  56. Niu, X.L., Liu, Y.G., Man, Y.C.: Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances. Int. J. Control 92(6), 1415–1425 (2019)

    MathSciNet  MATH  Google Scholar 

  57. Khoo, S.Y., Xie, L.H., Zhao, S.K., Man, Z.H.: Multi-surface sliding control for fast finite-time leader-follower consensus with high order SISO uncertain nonlinear agents. Int. J. Robust Nonlin. 24(16), 2388–2404 (2014)

    MathSciNet  MATH  Google Scholar 

  58. Yin, J.L., Khoo, S.Y., Man, Z.H.: Finite-time stability theorems of homogeneous stochastic nonlinear systems. Syst. Control Lett. 100, 6–17 (2017)

    MathSciNet  MATH  Google Scholar 

  59. Wang, Y., Song, Y., Krstic, M.: Adaptive finite time coordinated consensus for high-order multi-agent systems. Inf. Sci. 372, 392–406 (2016)

    MATH  Google Scholar 

  60. Yin, J.L., Khoo, S.Y., Man, Z.H., Yu, X.G.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47(12), 2671–2677 (2011)

    MathSciNet  MATH  Google Scholar 

  61. Yu, X., Yin, J.L., Khoo, S.Y.: Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems. Automatica 107, 183–189 (2019)

    MathSciNet  MATH  Google Scholar 

  62. Khoo, S., Yin, J.L., Man, Z.: Finite-time stabilization of stochastic nonlinear systems in strict-feedback form. Automatica 49(5), 1403–1410 (2013)

    MathSciNet  MATH  Google Scholar 

  63. Wang, H.Q., Liu, P.X.P., Bao, J.L., Xie, X.J., Li, S.: Adaptive neural output-feedback decentralized control for large-scale nonlinear systems with stochastic disturbances. IEEE Trans. Neural Netw. Lear. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2912082

    Article  Google Scholar 

  64. Wang, L.X.: Adaptive fuzzy systems and control: Design and stability analysis. Prentice-Hall, Englewood Cliffs, NJ (1994)

    Google Scholar 

  65. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)

    MATH  Google Scholar 

  66. Wang, H.Q., Liu, P.X.P., Xie, X.J., Liu, X.P., Hayat, T., Alsaadi, F.E.: Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator. Inf. Sci. (2018). https://doi.org/10.1016/j.ins.2018.04.011

    Article  Google Scholar 

  67. Qian, C., Lin, W.: Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)

    MathSciNet  MATH  Google Scholar 

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Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 61503223 and 61873137, and in part by SDUST Research Fund (No. 2015TDJH105).

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Fang Wang & Yan Zhang

  2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, People’s Republic of China

    Lili Zhang

  3. College of Computer Science and Technology, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    Jing Zhang

  4. College of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, 410000, China

    Yuanyuan Huang

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  1. Fang Wang
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  2. Yan Zhang
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  3. Lili Zhang
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  4. Jing Zhang
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  5. Yuanyuan Huang
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Correspondence to Fang Wang.

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Wang, F., Zhang, Y., Zhang, L. et al. Finite-Time Consensus of Stochastic Nonlinear Multi-agent Systems. Int. J. Fuzzy Syst. 22, 77–88 (2020). https://doi.org/10.1007/s40815-019-00769-w

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  • DOI: https://doi.org/10.1007/s40815-019-00769-w

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