Advertisement

Distributed Adaptive Dynamic Surface Containment Control for Uncertain Multiple Euler-Lagrange Systems

  • Yeong-Hwa Chang
  • Wei-Shou Chan
  • Chun-I Wu
Regular Paper Control Theory and Applications
  • 110 Downloads

Abstract

This paper investigates the distributed containment control for a class of uncertain multiple Euler- Lagrange systems. A directed graph is used to characterize the interactions among the leaders and followers. The proposed approach is based on an adaptive dynamic surface control, where the system uncertainties are approximately modelled by interval type-2 fuzzy neural networks. The adaptive laws of neuro-fuzzy parameters are derived from the Lyapunov stability analysis. The robust stability of the closed-loop system is guaranteed, and then all followers can converge into the convex hull spanned by the dynamic leaders. In this study, a systematic control scheme is proposed and several indexes are used for performance comparisons. Simulation results are also provided to reveal the superiority of the proposed distributed adaptive containment controller.

Keywords

Adaptive dynamic surface control containment control interval type-2 fuzzy neural network multiple Euler-Lagrange systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Y.-H. Chang, C.-W. Chang, C.-L. Chen, and C.-W. Tao, “Fuzzy sliding-mode formation control for multirobot systems: design and implementation,” IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 42, no. 2, pp. 444–457, April 2012. [click]CrossRefGoogle Scholar
  2. [2]
    J. Luo, J. Hu, D. Wu, and R. Li, “Opportunistic routing algorithm for relay node selection in wireless sensor networks,” IEEE Trans. on Industrial Informatics, vol. 11, no. 1, pp. 112–121, February 2015. [click]CrossRefGoogle Scholar
  3. [3]
    L. Zuo, W. Yan, R. Cui, and J. Gao, “A coverage algorithm for multiple autonomous surface vehicles in flowing environments,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 540–548, April 2016. [click]CrossRefGoogle Scholar
  4. [4]
    J. Luo, J. Hu, D. Wu, and R. Li, “Automatic restoration system for power distribution networks based on multi-agent systems,” IET Generation, Transmission & Distribution, vol. 11, no. 2, pp. 475–484, January 2017. [click]CrossRefGoogle Scholar
  5. [5]
    S. J. Yoo, “Distributed adaptive consensus tracking of a class of networked non-linear systems with parametric uncertainties,” IET Control Theory & Applications, vol. 7, no. 7, pp. 1049–1067, July 2013.MathSciNetCrossRefGoogle Scholar
  6. [6]
    J. Bai, G. Wen, Y. Song, A. Rahmani, and Y. Yu, “Distributed formation control of fractional-order multi-agent systems with relative damping and communication delay,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 85–94, February 2017. [click]CrossRefGoogle Scholar
  7. [7]
    J. Mei, W. Ren, and G. Ma, “Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph,” Automatica, vol. 48, no. 4, pp. 653–659, April 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Q. Ma and G. Miao, “Distributed containment control of linear multi-agent systems,” Neurocomputing, vol. 133, no. 10, pp. 399–403, June 2014. [click]CrossRefGoogle Scholar
  9. [9]
    C. Deng and G.-H. Yang, “Distributed adaptive faulttolerant containment control for a class of multi-agent systems with non-identical matching non-linear functions,” IET Control Theory & Applications, vol. 10, no. 3, pp. 273–281, January 2016. [click]MathSciNetCrossRefGoogle Scholar
  10. [10]
    X. Dong, L. Han, Q. Li, J. Chen, and Z. Ren, “Containment analysis and design for general linear multi-agent systems with time-varying delays,” Neurocomputing, vol. 173, Part 3, pp. 2062–2068, January 2016. [click]CrossRefGoogle Scholar
  11. [11]
    Z. Yang, X.-W. Mu, and K. Liu, “Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 442–449, February 2017. [click]CrossRefGoogle Scholar
  12. [12]
    Z. Meng, W. Ren, and Z. You, “Distributed finite-time attitude containment control for multiple rigid bodies,” Automatica, vol. 46, no. 12, pp. 2092–2099, December 2010. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Z. Meng, Z. Lin, and W. Ren, “Leader-follower swarm tracking for networked Lagrange systems,” Systems & Control Letters, vol. 61, no. 1, pp. 117–126, January 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    D. Yang, W. Ren, and X. Liu, “Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems,” Systems & Control Letters, vol. 72, pp. 44–52, October 2014. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    J. Mei, W. Ren, B. Li, and G. Ma, “Distributed containment control for multiple unknown second-order nonlinear systems with application to networked Lagrangian systems,” IEEE Trans. on Neural Networks and Learning Systems, vol. 26, no. 9, pp. 1885–1899, September 2015. [click]MathSciNetCrossRefGoogle Scholar
  16. [16]
    F.-J. Lin and P.-H. Chou, “Adaptive control of two-axis motion control system using interval type-2 fuzzy neural network,” IEEE Trans. on Industrial Electronics, vol. 56, no. 1, pp. 178–193, January 2009. [click]CrossRefGoogle Scholar
  17. [17]
    H. Tahayori, L. Livi, A. Sadeghian, and A. Rizzi, “Interval type-2 fuzzy set reconstruction based on fuzzy information-theoretic kernels,” IEEE Trans. on Fuzzy Systems, vol. 23, no. 4, pp. 1014–1029, August 2015. [click]CrossRefGoogle Scholar
  18. [18]
    A. Halder, A. Konar, R. Mandal, A Chakraborty, P. Bhowmik, N. R. Pal, and A. K. Nagar, “General and interval type-2 fuzzy face-space approach to emotion recognition,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 43, no. 3, pp. 587–605, May 2013. [click]CrossRefGoogle Scholar
  19. [19]
    C.-F. Juang and C.-Y. Chen, “Data-driven interval type-2 neural fuzzy system with high learning accuracy and improved model interpretability,” IEEE Trans. on Cybernetics, vol. 43, no. 6, pp. 1781–1795, December 2013. [click]CrossRefGoogle Scholar
  20. [20]
    S.-M. Chen and J.-A. Hong, “Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets and the TOPSIS method,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 44, no. 12, pp. 1665–1673, December 2014. [click]CrossRefGoogle Scholar
  21. [21]
    S. K. Raju and G. N. Pillai, “Design and implementation of type-2 fuzzy logic controller for DFIG-based wind energy systems in distribution networks,” IEEE Trans. on Sustainable Energy, vol. 7, no. 1, pp. 345–353, January 2016. [click]CrossRefGoogle Scholar
  22. [22]
    D. Swaroop, J. K. Hedrick, P. P. Yip, and J. C. Gerdes, “Dynamic surface control for a class of nonlinear systems,” IEEE Trans. on Automatic Control, vol. 45, no. 10, pp. 1893–1899, October 2000. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Y.-H. Chang, W.-S. Chan, and C.-W. Chang, “T-S fuzzy model based adaptive dynamic surface control for ball and beam system,” IEEE Trans. on Industrial Electronics, vol. 60, no. 6, pp. 2251–2263, June 2013. [click]CrossRefGoogle Scholar
  24. [24]
    L. Zhang, C. Hua, and X. Guan, “Distributed output feedback consensus tracking prescribed performance control for a class of non-linear multi-agent systems with unknown disturbances,” IET Control Theory & Applications, vol. 10, no. 8, pp. 877–883, May 2016. [click]MathSciNetCrossRefGoogle Scholar
  25. [25]
    M.-S. Qian, B. Jiang, and H. H.-T. Liu, “Dynamic surface active fault tolerant control design for the attitude control systems of UAV with actuator fault,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 723–732, June 2016. [click]CrossRefGoogle Scholar
  26. [26]
    S. Gao, H. Dong, B. Ning, and X. Yao, “Single-parameterlearning- based fuzzy fault-tolerant output feedback dynamic surface control of constrained-input nonlinear systems,” Information Sciences, vol. 385-386, pp. 378–394, April 2017. [click]CrossRefGoogle Scholar
  27. [27]
    Y.-H. Chang and W.-S. Chan, “Adaptive dynamic surface control for uncertain nonlinear systems with interval type-2 fuzzy neural networks,” IEEE Trans. on Cybernetics, vol. 44, no. 2, pp. 293–304, February 2014. [click]MathSciNetCrossRefGoogle Scholar
  28. [28]
    S. S. Ge, C. C. Hang, T. H. Lee, and T. Zhang, Stable adaptive neural network control, New Yrk: Springer.Google Scholar
  29. [29]
    G. Fu, L. Ou, and W. Zhang, “Robust adaptive tracking control of MIMO nonlinear systems in the presence of actuator hysteresis,” International Journal of Systems Science, vol. 47, no. 10, pp. 2359–2369, 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringChang Gung UniversityGuishan, TaoyuanTaiwan
  2. 2.Department of Electrical EngineeringMing Chi University of TechnologyNew Taipei CityTaiwan
  3. 3.National Chung-Shan Institute of Science and TechnologyTaoyuanTaiwan
  4. 4.Department of Electrical EngineeringChang Gung UniversityGuishan, TaoyuanTaiwan

Personalised recommendations