Skip to main content
SpringerLink
Log in

Fixed-time adaptive event-triggered tracking control of uncertain nonlinear systems

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper addresses the event-triggered tracking control problem of nonlinear systems with predefined performance in a fixed-time environment. Unlike the existing event-triggered schemes, the developed triggering mechanism only compares the difference between the signal to be transmitted and the holding signal. The proposed control method also considers the response of the triggering mechanism. In order to achieve prescribed control performance under the condition of unmatched uncertainties and uncertain gain functions, a new adaptive fixed-time control strategy is proposed by introducing an error transformation scheme. The proposed control method under the event-triggered framework can reduce the amount of control signals transmitted while ensuring that the system output tracking error converges to a small neighborhood close to zero within a fixed-time frame. The results of two examples, including comparative studies and a practical application, show the effectiveness of the proposed control method.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Baillieul, J., Antsaklis, P.J.: Control and communication challenges in networked real-time systems. Proc. IEEE 95(1), 9–28 (2007)

    Google Scholar 

  2. Elahi, A., Alfi, A.: Finite-time stability analysis of uncertain network-based control systems under random packet dropout and varying network delay. Nonlinear Dyn. 91(1), 713–731 (2018)

    MathSciNet  MATH  Google Scholar 

  3. Yu, Y., Yuan, Y., Yang, H.J., Liu, H.P.: Nonlinear sampled-data ESO-based active disturbance rejection control for networked control systems with actuator saturation. Nonlinear Dyn. 95(2), 1415–1434 (2019)

    Google Scholar 

  4. Ling, S., Wang, H.Q., Liu, P.X.: Adaptive fuzzy dynamic surface control of flexible-joint robot systems with input saturation. IEEE/CAA J. Autom. Sin. 6(1), 97–106 (2019)

    MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  6. Zhao, X., Wang, X., Zong, G.: Adaptive neural backstepping control design for a class of non-smooth nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2018.2875947

    Article  Google Scholar 

  7. Zhao, X., Wang, X., Ma, L., Zong, G.: Fuzzy-approximation-based asymptotic tracking control for a class of uncertain switched nonlinear systems. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2912138

    Article  Google Scholar 

  8. Chen, B., Zhang, H., Liu, X.P., 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 

  9. Ling, S., Wang, H., Liu, P.X.: Adaptive fuzzy tracking control of flexible-joint robots based on command filtering. IEEE Trans. Ind. Electron. 67(5), 4046–4055 (2020)

    Google Scholar 

  10. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)

    MathSciNet  MATH  Google Scholar 

  11. Postoyan, R., Tabuada, P., Nesic, D., Anta, A.: A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Autom. Control 60(4), 982–996 (2015)

    MathSciNet  MATH  Google Scholar 

  12. Adaldo, A., Alderisio, F., Liuzza, D., Shi, G., Dimarogonas, D. V., Bernardo, M., Johansson, K. H.: Event-triggered pinning control of complex networks with switching topologies. In: Proceedings of 53rd Annual IEEE CDC, pp. 2783–2788 (2014)

  13. Adaldo, A., Alderisio, F., Liuzza, D., Shi, G., Dimarogonas, D.V., di Bernardo, M., Johansson, K.H.: Event-triggered pinning control of switching networks. IEEE Trans. Control Netw. Syst. 2(2), 204–213 (2015)

    MathSciNet  MATH  Google Scholar 

  14. Xing, L., Wen, C., Liu, Z., Su, H., Cai, J.: Event-triggered adaptive control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 62(4), 2071–2076 (2017)

    MathSciNet  MATH  Google Scholar 

  15. Xing, L., Wen, C., Liu, Z., Su, H., Cai, J.: Event-triggered output feedback control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 64(1), 290–297 (2019)

    MathSciNet  MATH  Google Scholar 

  16. Li, Y.X., Yang, G.H.: Model-based adaptive event-triggered control of strict-feedback nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(4), 1033–1045 (2018)

    MathSciNet  Google Scholar 

  17. Li, Y.X., Yang, G.H.: Event-triggered adaptive backstepping control for parametric strict-feedback nonlinear systems. Int. J. Robust Nonlinear Control 28(3), 976–1000 (2018)

    MathSciNet  MATH  Google Scholar 

  18. Zhang, C.H., Yang, G.H.: Event-triggered adaptive output feedback control for a class of uncertain nonlinear systems with actuator failures. IEEE Trans. Cybern. 50(1), 201–210 (2019)

    Google Scholar 

  19. Zhang, C.H., Yang, G.H.: Event-triggered control for a class of strict-feedback nonlinear systems. Int. J. Robust Nonlinear Control 29(7), 2112–2124 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Huang, Y., Liu, Y.: Practical tracking via adaptive event-triggered feedback for uncertain nonlinear systems. IEEE Trans. Autom. Control 64(9), 3920–3927 (2019)

    MathSciNet  MATH  Google Scholar 

  21. Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)

    MathSciNet  MATH  Google Scholar 

  22. Levant, A.: Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence. IEEE Trans. Autom. Control 46(9), 1447–1451 (2001)

    MathSciNet  MATH  Google Scholar 

  23. Yu, S., Yu, X., Shirinzadeh, B., et al.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)

    MathSciNet  MATH  Google Scholar 

  24. Wang, H.Q., Bai, W., Liu, P.X.: Finite-time adaptive fault-tolerant control for nonlinear systems with multiple faults. IEEE/CAA J. Autom. Sin. 6(6), 1417–1427 (2019)

    MathSciNet  Google Scholar 

  25. Fang, L., Ma, L., Ding, S., Zhao, D.: Finite-time stabilization for a class of high-order stochastic nonlinear systems with an output constraint. Appl. Math. Comput. 358, 63–79 (2019)

    MathSciNet  MATH  Google Scholar 

  26. Wang, H.Q., Liu, P.X., Zhao, X., Liu, X.: 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 

  27. Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)

    MathSciNet  MATH  Google Scholar 

  28. Zuo, Z., Tian, B., Defoort, M., Ding, Z.: Fixed-time consensus tracking for multi-agent systems with high-order integrator dynamics. IEEE Trans. Autom. Control 63(2), 563–570 (2018)

    MATH  Google Scholar 

  29. Zuo, Z.: Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54, 305–309 (2015)

    MathSciNet  MATH  Google Scholar 

  30. Zuo, Z.: Non-singular fixed-time terminal sliding mode control of nonlinear systems. IET Control Theory Appl. 9(4), 545–552 (2015)

    MathSciNet  Google Scholar 

  31. Ning, B., Han, Q.L., Zuo, Z.: Practical fixed-time consensus for integrator-type multi-agent systems: a time base generator approach. Automatica 105, 406–414 (2019)

    MathSciNet  MATH  Google Scholar 

  32. Basin, M., Panathula, C.B., Shtessel, Y.: Multivariable continuous fixed-time second-order sliding mode control: design and convergence time estimation. IET Control Theory Appl. 11(8), 1104–1111 (2017)

    MathSciNet  Google Scholar 

  33. Meng, D., Zuo, Z.: Signed-average consensus for networks of agents: a nonlinear fixed-time convergence protocol. Nonlinear Dyn. 85(1), 155–165 (2016)

    MathSciNet  MATH  Google Scholar 

  34. Song, Y., Wang, Y., Holloway, J., Krstic, M.: Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica 83, 243–251 (2017)

    MathSciNet  MATH  Google Scholar 

  35. Song, Y., Wang, Y., Krstic, M.: Time-varying feedback for stabilization in prescribed finite time. Int. J. Robust Nonlinear Control 29(3), 618–633 (2019)

    MathSciNet  MATH  Google Scholar 

  36. Wang, Y., Song, Y.: Leader-following control of high-order multiagent systems under directed graphs: pre-specified finite time approach. Automatica 87, 113–120 (2018)

    MathSciNet  MATH  Google Scholar 

  37. Wang, Y., Song, Y., Hill, D.J., Krstic, M.: Prescribed-time consensus and containment control of networked multiagent systems. IEEE Trans. Cybern. 49(4), 1138–1147 (2019)

    Google Scholar 

  38. Jin, X.: Adaptive fixed-time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions. IEEE Trans. Autom. Control 64(7), 3046–3053 (2019)

    MathSciNet  MATH  Google Scholar 

  39. Liu, J., Zhang, Y., Sun, C., Yu, Y.: Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered control. Inf. Sci. 480, 261–272 (2019)

    MathSciNet  Google Scholar 

  40. Liu, J., Yu, Y., Wang, Q., Sun, C.: Fixed-time event-triggered consensus control for multi-agent systems with nonlinear uncertainties. Neurocomputing 260, 497–504 (2017)

    Google Scholar 

  41. Liu, J., Zhang, Y., Yu, Y., Sun, C.: Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications. IEEE Trans. Syst. Man Cybern. Syst. (2018). https://doi.org/10.1109/TSMC.2018.2876334

    Article  Google Scholar 

  42. Rong, N., Wang, Z.: Fixed-time stabilization for IT2 T-S fuzzy interconnected systems via event-triggered mechanism: an exponential gain method. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2904192

    Article  Google Scholar 

  43. Wang, Y.Y., Hu, J.B., Wang, J.H., Xing, X.B.: Adaptive neural novel prescribed performance control for non-affine pure-feedback systems with input saturation. Nonlinear Dyn. 93(3), 1241–1259 (2018)

    MATH  Google Scholar 

  44. Hua, C., Zhang, L., Guan, X.: Decentralized output feedback adaptive NN tracking control for time-delay stochastic nonlinear systems with prescribed performance. IEEE Trans. Neural Netw. Learn. Syst. 26(11), 2749–2759 (2015)

    MathSciNet  Google Scholar 

  45. Wang, M., Wang, C., Shi, P., Liu, X.: Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2564–2576 (2016)

    MathSciNet  Google Scholar 

  46. Huang, J., Wen, C., Wang, W., Song, Y.D.: Design of adaptive finite time controllers for nonlinear uncertain systems based on given transient specifications. Automatica 31, 395–404 (2016)

    MathSciNet  MATH  Google Scholar 

  47. Zhai, D., Xi, C., An, L., Dong, J., Zhang, Q.: Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1257–1269 (2017)

    Google Scholar 

  48. Song, Y., Wang, Y., Wen, C.: Adaptive fault-tolerant PI tracking control with guaranteed transient and steady-state performance. IEEE Trans. Autom. Control 62(1), 481–487 (2017)

    MathSciNet  MATH  Google Scholar 

  49. Zhang, C., Ma, G.F., Sun, Y.C., Li, C.J.: Prescribed performance adaptive attitude tracking control for flexible spacecraft with active vibration suppression. Nonlinear Dyn. 96(3), 1909–1926 (2019)

    Google Scholar 

  50. Zhao, K., Song, Y.: Removing the feasibility conditions imposed on tracking control designs for state-constrained strict-feedback systems. IEEE Trans. Autom. Control 64(3), 1265–1272 (2019)

    MathSciNet  MATH  Google Scholar 

  51. Zhu, Y., Qiao, J., Guo, L.: Adaptive sliding mode disturbance observer-based composite control with prescribed performance of space manipulators for target capturing. IEEE Trans. Ind. Electron. 66(3), 1973–1983 (2019)

    Google Scholar 

  52. Wang, H., Shi, P., Li, H., Zhou, Q.: Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Trans. Cybern. 47(10), 3075–3087 (2017)

    Google Scholar 

  53. Wang, C., Lin, Y.: Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems. Automatica 54, 16–24 (2015)

    MathSciNet  MATH  Google Scholar 

  54. Wang, H., Chen, B., Lin, C.: Adaptive neural tracking control for a class of stochastic nonlinear systems. Int. J. Robust Nonlinear Control 24(7), 1262–1280 (2014)

    MathSciNet  MATH  Google Scholar 

  55. Zhu, Z., Xia, Y., Fu, M.: Attitude stabilization of rigid spacecraft with finite-time convergence. Int. J. Robust Nonlinear Control 21(6), 686–702 (2011)

    MathSciNet  MATH  Google Scholar 

  56. Zuo, Z., Tie, L.: A new class of finite-time nonlinear consensus protocols for multi-agent systems. Int. J. Control 87(2), 363–370 (2014)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities under Grant 2019YJS149.

Author information

Authors and Affiliations

  1. School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Song Ling & Huanqing Wang

  2. Department of Mathematics, Bohai University, Jinzhou, 121000, China

    Huanqing Wang

  3. Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Peter Xiaoping Liu

Authors
  1. Song Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huanqing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Xiaoping Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Song Ling, Huanqing Wang or Peter Xiaoping Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ling, S., Wang, H. & Liu, P.X. Fixed-time adaptive event-triggered tracking control of uncertain nonlinear systems. Nonlinear Dyn 100, 3381–3397 (2020). https://doi.org/10.1007/s11071-020-05578-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05578-7

Keywords

Search

Navigation