Skip to main content
SpringerLink
Log in

Structure-free containment control for uncertain underactuated multiple Euler-Lagrange systems

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This article studies the problem of structure-free distributed containment control for uncertain underactuated multiple Euler-Lagrange systems (MELSs) considering disturbances by using a layered approach. First, the second layer is the virtual layer constructed artificially for hierarchical control. We move all virtual nodes to the convex hull formed by leaders in the first layer by implementing containment control algorithms on all virtual nodes. Then, the third layer is the following layer, and we propose an adaptive robust tracking controller to ensure that each follower in the third layer tracks the corresponding virtual node in the second layer. So far, the underactuated MELSs can achieve containment control. Furthermore, through the theoretical derivation, sufficient conditions are obtained to achieve the objective of structure-free containment control. Finally, the effectiveness of the proposed stratified structure-free containment control method is verified by a simulation example.

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

Similar content being viewed by others

References

  1. Ma L F, Wang Z D, Han Q-L, et al. Consensus control of stochastic multi-agent systems: a survey. Sci China Inf Sci, 2017, 60: 120201

    Article  MathSciNet  Google Scholar 

  2. Martin S, Girard A, Fazeli A, et al. Multiagent flocking under general communication rule. IEEE Trans Control Netw Syst, 2014, 1: 155–166

    Article  MathSciNet  MATH  Google Scholar 

  3. Wen G X, Chen C L P, Dou H, et al. Formation control with obstacle avoidance of second-order multi-agent systems under directed communication topology. Sci China Inf Sci, 2019, 62: 192205

    Article  MathSciNet  Google Scholar 

  4. Chen J, Gan M G, Huang J, et al. Formation control of multiple Euler-Lagrange systems via null-space-based behavioral control. Sci China Inf Sci, 2016, 59: 010202

    Article  Google Scholar 

  5. Wang S, Jin X, Mao S, et al. Model-free event-triggered optimal consensus control of multiple Euler-Lagrange systems via reinforcement learning. IEEE Trans Netw Sci Eng, 2021, 8: 246–258

    Article  MathSciNet  Google Scholar 

  6. Zhao K, Song Y, Ma T, et al. Prescribed performance control of uncertain Euler-Lagrange systems subject to full-state constraints. IEEE Trans Neural Netw Learn Syst, 2018, 29: 3478–3489

    Article  MathSciNet  Google Scholar 

  7. Ashrafiuon H, Erwin R S. Sliding mode control of underactuated multibody systems and its application to shape change control. Int J Control, 2008, 81: 1849–1858

    Article  MathSciNet  MATH  Google Scholar 

  8. Olfati-Saber R. Normal forms for underactuated mechanical systems with symmetry. IEEE Trans Automat Contr, 2002, 47: 305–308

    Article  MathSciNet  MATH  Google Scholar 

  9. Lu B, Fang Y, Sun N. Modeling and nonlinear coordination control for an underactuated dual overhead crane system. Automatica, 2018, 91: 244–255

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu Z, Yan Q. Controller design and simulation of underactuated pendulum. In: Proceedings of the IEEE Chinese Control and Decision Conference (CCDC), 2011. 2767–2771

    Google Scholar 

  11. Huang J, Ri S, Fukuda T, et al. A disturbance observer based sliding mode control for a class of underactuated robotic system with mismatched uncertainties. IEEE Trans Automat Contr, 2019, 64: 2480–2487

    Article  MathSciNet  MATH  Google Scholar 

  12. Lu B, Fang Y, Sun N. Continuous sliding mode control strategy for a class of nonlinear underactuated systems. IEEE Trans Automat Contr, 2018, 63: 3471–3478

    Article  MathSciNet  MATH  Google Scholar 

  13. Nersesov S G, Ashrafiuon H, Ghorbanian P. On estimation of the domain of attraction for sliding mode control of underactuated nonlinear systems. Int J Robust Nonlinear Control, 2014, 24: 811–824

    Article  MathSciNet  MATH  Google Scholar 

  14. Sarras I, Acosta J, Ortega R, et al. Constructive immersion and invariance stabilization for a class of underactuatedmechanical systems. Automatica, 2013, 49: 1442–1448

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu R, Özgüner Ü. Sliding mode control of a class of underactuated systems. Automatica, 2008, 44: 233–241

    Article  MathSciNet  MATH  Google Scholar 

  16. Yoo S J, Park B S. Guaranteed performance design for distributed bounded containment control of networked uncertain underactuated surface vessels. J Franklin Institute, 2017, 354: 1584–1602

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu Z W, Hou H, Wang Y W. Formation-containment control of multiple underactuated surface vessels with sampling communication via hierarchical sliding mode approach. ISA Trans, 2019, 124: 458–467

    Article  Google Scholar 

  18. Cai H, Huang J. The leader-following consensus for multiple uncertain euler-lagrange systems with an adaptive distributed observer. IEEE Trans Automat Contr, 2016, 61: 3152–3157

    Article  MathSciNet  MATH  Google Scholar 

  19. Lu M, Liu L. Leader-following consensus of multiple uncertain euler-lagrange systems with unknown dynamic leader. IEEE Trans Automat Contr, 2019, 64: 4167–4173

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang L, He H, Zeng Z, et al. Model-independent formation tracking of multiple Euler-Lagrange systems via bounded inputs. IEEE Trans Cybern, 2021, 51: 2813–2823

    Article  Google Scholar 

  21. Wei B, Xiao F, Fang F, et al. Velocity-free event-triggered control for multiple Euler-Lagrange systems with communication time delays. IEEE Trans Automat Contr, 2021, 66: 5599–5605

    Article  MathSciNet  MATH  Google Scholar 

  22. Hua Y, Dong X, Li Q, et al. Distributed time-varying formation robust tracking for general linear multiagent systems with parameter uncertainties and external disturbances. IEEE Trans Cybern, 2017, 47: 1959–1969

    Article  Google Scholar 

  23. Li D, Zhang W, He W, et al. Two-layer distributed formation-containment control of multiple Euler-Lagrange systems by output feedback. IEEE Trans Cybern, 2019, 49: 675–687

    Article  Google Scholar 

  24. Bidram A, Davoudi A, Lewis F L, et al. Distributed cooperative secondary control of microgrids using feedback linearization. IEEE Trans Power Syst, 2013, 28: 3462–3470

    Article  Google Scholar 

  25. Spong M W, Hutchinson S, Vidyasagar M. Robot Dynamics and Control. Hoboken: John Wiley and Sons, 2004

    Google Scholar 

  26. Ren W, Cao Y. Distributed Coordination of Multi-Agent Networks: Emergent Problems, Models, and Issues. London: Springer-Verlag, 2011

    Book  MATH  Google Scholar 

  27. Kim T, Lee C, Shim H. Completely decentralized design of distributed observer for linear systems. IEEE Trans Automat Contr, 2020, 65: 4664–4678

    Article  MathSciNet  MATH  Google Scholar 

  28. Su Y, Huang J. Cooperative output regulation with application to multi-agent consensus under switching network. IEEE Trans Syst Man Cybern B, 2012, 42: 864–875

    Article  Google Scholar 

  29. Shtessel Y, Taleb M, Plestan F. A novel adaptive-gain supertwisting sliding mode controller: methodology and application. Automatica, 2012, 48: 759–769

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61991412, 62273159, U22A6007) and Program for HUST Academic Frontier Youth Team (Grant No. 2018QYTD07).

Author information

Authors and Affiliations

  1. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Housheng Su, Yali Wu & Liren Zhang

  2. State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Xia Chen

Authors
  1. Housheng Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yali Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liren Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xia Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xia Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, H., Wu, Y., Zhang, L. et al. Structure-free containment control for uncertain underactuated multiple Euler-Lagrange systems. Sci. China Inf. Sci. 66, 212203 (2023). https://doi.org/10.1007/s11432-022-3711-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-022-3711-1

Keywords

Search

Navigation