Skip to main content
SpringerLink
Log in

Distributed adaptive PI consensus tracking control for output-constrained nonlinear multiagent systems with unknown control directions

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

Abstract

This paper investigates the distributed adaptive PI consensus tracking control for output-constrained nonlinear multiagent systems (MASs) with unknown control directions and unknown time-varying actuator faults under the directed graph. Firstly, an auxiliary filter network is constructed to estimate the output of the leader. Then, by introducing a nonlinear state transformation function, the asymmetric constraints on agents’ outputs can be achieved with unconstrained initial conditions. Furthermore, based on the Nussbaum-type function, a distributed adaptive PI controller is designed by utilizing the constructed generalized error for nonlinear MASs with unknown time-varying control directions caused by actuator faults. The proposed control scheme can guarantee that all signals in the closed-loop system are bounded and the distributed asymptotic consensus tracking is achieved. Finally, a simulation example illustrates the effectiveness of the proposed control strategy.

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
Fig. 12

Similar content being viewed by others

Data Availability

The datasets supporting the conclusions of this article are included within the article.

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Dimarogonas, D.V., Frazzoli, E., Johansson, K.H.: Distributed event-triggered control for multi-agent systems. IEEE Trans. Autom. Control 57(5), 1291–1297 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Su, S.Z., Lin, Z.L.: Distributed consensus control of multi-agent systems with higher order agent dynamics and dynamically changing directed interaction topologies. IEEE Trans. Autom. Control 61(2), 515–519 (2016)

    MathSciNet  MATH  Google Scholar 

  4. Zhang, X.F., Liu, L., Feng, G.: Leader-follower consensus of time-varying nonlinear multi-agent systems. Automatica 52, 8–14 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yoo, S.J.: Distributed consensus tracking of a class of asynchronously switched nonlinear multi-agent systems. Automatica 87, 421–427 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hua, C.C., Li, K., Guan, X.P.: Leader-following output consensus for high order nonlinear multiagent systems. IEEE Trans. Autom. Control 64(3), 1156–1161 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu, G.L., Sun, Q.Y., Wang, R., Huang, Y.J.: Reduced-order observer-based fuzzy adaptive dynamic event-triggered consensus control for multi-agent systems with communication faults. Nonlinear Dyn. 110, 1421–1435 (2022)

    Article  Google Scholar 

  8. Huang, J.S., Song, Y.D., Wang, W., Wen, C.Y., Li, G.Q.: Smooth control design for adaptive leader-following consensus control of a class of high-order nonlinear systems with time-varying reference. Automatica 83, 361–367 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  9. Huang, J.S., Wang, W., Wen, C.Y., Zhou, J., Li, G.Q.: Distributed adaptive leader-follower and leaderless consensus control of a class of strict-feedback nonlinear systems: a unified approach. Automatica 118, 109021 (2020)

  10. Lui, D.G., Petrillo, A., Santini, S.: Leader tracking control for heterogeneous uncertain nonlinear multi-agent systems via a distributed robust adaptive PID strategy. Nonlinear Dyn. 108, 363–378 (2022)

    Article  Google Scholar 

  11. Wang, C.L., Wen, C.Y., Hu, Q.L.: Event-triggered adaptive control for a class of nonlinear systems with unknown control direction and sensor faults. IEEE Trans. Autom. Control 65(2), 763–770 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  12. Huang, J.S., Wang, W., Wen, C.Y., Zhou, J.: Adaptive control of a class of strict-feedback time-varying nonlinear systems with unknown control coefficients. Automatica 93, 98–105 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang, Z.R., Song, Y.D., Wen, C.Y.: Adaptive decentralized output-feedback control dealing with static/dynamic interactions and different unknown subsystem control directions. IEEE Trans. Autom. Control 66(8), 3818–3824 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, W., Wen, C.Y., Guo, L., Xing, L.T.: Adaptive consensus control for nonlinear multiagent systems with unknown control directions using event-triggered communication. IEEE Trans. Cybern. 52(5), 3057–3068 (2022)

    Article  Google Scholar 

  15. Wang, C.L., Wen, C.Y., Guo, L.: Adaptive consensus control for nonlinear multiagent systems with unknown control directions and time-varying actuator faults. IEEE Trans. Autom. Control 66(9), 4222–4229 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. Khalil, H.K.: Universal integral controllers for minimum-phase nonlinear systems. IEEE Trans. Autom. Control 45(3), 490–494 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chang, W.-D., Hwang, R.-C., Hsieh, J.-G.: A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach. J. Process Control 12(2), 233–242 (2002)

    Article  Google Scholar 

  18. Song, Y.D., Wang, Y.J., Wen, C.Y.: Adaptive fault-tolerant PI tracking control with guaranteed transient and steady-state performance. IEEE Trans. Autom. Control 62(1), 481–487 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  19. Song, Y.D., Guo, J.X., Huang, X.C.: Smooth neuroadaptive PI tracking control of nonlinear systems with unknown and nonsmooth actuation characteristics. IEEE Trans. Neural Netw. Learn. Syst. 28(9), 2183–2195 (2016)

    MathSciNet  Google Scholar 

  20. Sun, H.B., Zong, G.D., Ahn, C.K.: Quantized decentralized adaptive neural network PI tracking control for uncertain interconnected nonlinear systems with dynamic uncertainties. IEEE Trans. Syst. Man Cybern. 51(5), 3111–3124 (2021)

    Article  Google Scholar 

  21. Gao, X.F., Li, X.C., Xiao, J.C., Hao, L.N.: Robust PI-Type Output Feedback Control of Unknown Nonlinear Systems. IEEE Trans. Ind. Electron. 69(9), 9396–9405 (2021)

    Article  Google Scholar 

  22. Liang, H.J., Zhang, Y.H., Huang, T.W., Ma, H.: Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. 50(5), 1810–1819 (2020)

    Article  Google Scholar 

  23. Zhang, L.L., Zhu, L.C., Hua, C.C.: Practical prescribed time control based on high-order fully actuated system approach for strong interconnected nonlinear systems. Nonlinear Dyn. 110, 3535–3545 (2022)

    Article  Google Scholar 

  24. Liu, Y.L., Ma, H.J., Ma, H.: Adaptive fuzzy fault-tolerant control for uncertain nonlinear switched stochastic systems with time-varying output constraints. IEEE Trans. Fuzzy Syst. 26(5), 2487–2498 (2018)

    Article  Google Scholar 

  25. Li, Y.M., Liu, Y.J., Tong, S.C.: Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints. IEEE Trans. Neural Netw. Learn. Syst. 33(7), 3131–3145 (2022)

    Article  MathSciNet  Google Scholar 

  26. Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov Functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Liu, Y.J., Tong, S.C.: Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64, 70–75 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhao, K., Song, Y.D., Zhang, Z.R.: Tracking control of MIMO nonlinear systems under full state constraints: A single-parameter adaptation approach free from feasibility conditions. Automatica 107, 52–60 (2019)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  30. Song, Y.D., Zhou, S.Y.: Tracking control of uncertain nonlinear systems with deferred asymmetric time-varying full state constraints. Automatica 98, 314–322 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhang, L.L., Zhu, L.C., Hua, C.C., Qian, C.: Adaptive decentralized control for interconnected time-delay uncertain nonlinear systems with different unknown control directions and deferred full-state constraints. IEEE Trans. Neural Networks Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3171518

  32. Zhao, K., Song, Y.D., Chen, C.L.P., Chen, L.: Adaptive asymptotic tracking with global performance for nonlinear systems with unknown control directions. IEEE Trans. Autom. Control 67(3), 1566–1573 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  33. Cao, Y., Cao, J.F., Song, Y.D.: Practical prescribed time tracking control over infinite time interval involving mismatched uncertainties and non-vanishing disturbances. Automatica 136, 110050 (2022)

  34. Cui, Q., Cao, H.W., Wang, Y.J., Song, Y.D.: Prescribed time tracking control of constrained Euler-Lagrange systems: An adaptive proportional-integral solution. Int. J. Robust Nonlin. Control 32(18), 9723–9741 (2022)

    Article  MathSciNet  Google Scholar 

  35. Sun, Y., Shi, P., Lim, C.C.: Adaptive consensus control for output-constrained nonlinear multi-agent systems with actuator faults. J. Frankl. Inst. 359(6), 4216–4232 (2022)

  36. Fan, D.B., Zhang, X.F., Liu, S., Chen, X.D.: Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions. J. Frankl. Inst. 358(16), 8270–8287 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  37. Wang, G., Wang, C.L., Cai, X.: Consensus control of output-constrained multiagent systems with unknown control directions under a directed graph. Int. J. Robust Nonlin. Control 30(5), 1802–1818 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  38. Fan, B., Yang, Q.M., Jagannathan, S., Sun, Y.X.: Output-constrained control of nonaffine multiagent systems with partially unknown control directions. IEEE Trans. Autom. Control 64(9), 3936–3942 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  39. Mohit, M., Shahrokhi, M.: Adaptive fixed-time consensus control for a class of non-strict feedback multi-agent systems subject to input nonlinearities, state constraints, unknown control directions, and actuator faults. Eur. J. Control 66, 100649 (2022)

Download references

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62273297, Grant 62103353, Grant 61825304, and Grant 6182500417; in part by the Top Young Talents of Education Department of Hebei Province under Grant BJ2021041; and in part by Hebei innovation capability improvement plan project 22567619H.

Author information

Authors and Affiliations

  1. Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Lingchen Zhu, Liuliu Zhang & Changchun Hua

Authors
  1. Lingchen Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liuliu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changchun Hua
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liuliu Zhang.

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

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, L., Zhang, L. & Hua, C. Distributed adaptive PI consensus tracking control for output-constrained nonlinear multiagent systems with unknown control directions. Nonlinear Dyn 111, 17179–17191 (2023). https://doi.org/10.1007/s11071-023-08748-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08748-5

Keywords

Search

Navigation