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Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator

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Abstract

This paper investigates the cooperative output regulation problem of linear multi-agent systems with a linear exogenous system (exo-system). The network topology is described by a directed graph which contains a directed spanning tree with the exo-system as the root. Aiming at improving the transient performance of the multi-agent systems, a dynamic control law is developed by the composite nonlinear feedback (CNF) control technique. In particular, a distributed dynamic compensator independent of the interaction on the compensator states of agents among the network, is adopted. The solvability condition for the cooperative output regulation problem is obtained using the small-gain theory, which will not be destroyed by adding the nonlinear feedback part of the CNF control law. It is also shown that in the case with the exo-system not diverging exponentially, the small-gain condition can be guaranteed using the low-gain design. Finally, simulation results illustrate that the proposed CNF control law improves the transient performance for the cooperative output regulation of linear multi-agent systems.

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References

  1. Grip, H. F., Yang, T., Saberi, A., & Stoorvogel, A. A. (2012). Output synchronization for heterogeneous networks of non-introspective agents. Automatica, 48(10), 2444–2453.

    Article  MathSciNet  MATH  Google Scholar 

  2. Hong, Y., Wang, X., & Jiang, Z.-P. (2013). Distributed output regulation of leader-follower multi-agent systems. International Journal of Robust and Nonlinear Control, 23(1), 48–66.

    Article  MathSciNet  MATH  Google Scholar 

  3. Lu, M., & Liu, L. (2017). Cooperative output regulation of linear multi-agent systems by a novel distributed dynamic compensator. IEEE Transactions on Automatic Control, 62(12), 6481–6488.

    Article  MathSciNet  MATH  Google Scholar 

  4. Su, Y., & Huang, J. (2012). Cooperative output regulation of linear multi-agent systems. IEEE Transactions on Automatic Control, 57(4), 1062–1066.

    Article  MathSciNet  MATH  Google Scholar 

  5. Su, Y., & Huang, J. (2012). Cooperative output regulation of linear multi-agent systems by output feedback. Systems & Control Letters, 61(12), 1248–1253.

    Article  MathSciNet  MATH  Google Scholar 

  6. Wang, X., Hong, Y., Huang, J., & Jiang, Z.-P. (2010). A distributed control approach to a robust output regulation problem for multi-agent linear systems. IEEE Transactions on Automatic control, 55(12), 2891–2895.

    Article  MathSciNet  MATH  Google Scholar 

  7. Yu, X., & Liu, L. (2016). Distributed formation control of nonholonomic vehicles subject to velocity constraints. IEEE Transactions on Industrial Electronics, 63(2), 1289–1298.

    Article  MathSciNet  Google Scholar 

  8. Lin, Z., Pachter, M., & Banda, S. (1998). Toward improvement of tracking performance nonlinear feedback for linear systems. International Journal of Control, 70(1), 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  9. Turner, M. C., Postlethwaite, I., & Walker, D. J. (2000). Non-linear tracking control for multivariable constrained input linear systems. International Journal of Control, 73(12), 1160–1172.

  10. Chen, B. M., Lee, T. H., Peng, K., & Venkataramanan, V. (2003). Composite nonlinear feedback control for linear systems with input saturation: theory and an application. IEEE Transactions on Automatic Control, 48(3), 427–439.

    Article  MathSciNet  MATH  Google Scholar 

  11. He, Y., Chen, B. M., & Wu, C. (2005). Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation. Systems & Control Letters, 54(5), 455–469.

    Article  MathSciNet  MATH  Google Scholar 

  12. Jafari, E., & Binazadeh, T. (2019). Observer-based improved composite nonlinear feedback control for output tracking of time-varying references in descriptor systems with actuator saturation. ISA Transactions, 91, 1–10.

    Article  Google Scholar 

  13. Lu, T., & Lan, W. (2019). Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation. International Journal of Control, 92(9), 2170–2177.

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, C., Yu, X., & Lan, W. (2014). Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control. International Journal of Control, 87(10), 1985–1997.

    MathSciNet  MATH  Google Scholar 

  15. Zhang, B., & Lan, W. (2013). Improving transient performance for output regulation problem of linear systems with input saturation. International Journal of Robust and Nonlinear Control, 23(10), 1087–1098.

    Article  MathSciNet  MATH  Google Scholar 

  16. Lei, C., Sun, W., & Yeow, J.T. (2016). A distributed output regulation problem for multi-agent linear systems with application to leader-follower robot’s formation control. In 2016 35th Chinese Control Conference (CCC), pp. 614–619. IEEE.

  17. Hou, Z., & Fantoni, I. (2017). Interactive leader-follower consensus of multiple quadrotors based on composite nonlinear feedback control. IEEE Transactions on Control Systems Technology, 26(5), 1732–1743.

    Article  Google Scholar 

  18. Godsil, C., & Royle, G. F. (2001). Algebraic Graph Theory (Vol. 207). New York: Springer.

    MATH  Google Scholar 

  19. Francis, B. A. (1977). The linear multivariable regulator problem. SIAM Journal on Control and Optimization, 15(3), 486–505.

    Article  MathSciNet  MATH  Google Scholar 

  20. Francis, B. A., & Wonham, W. M. (1976). The internal model principle of control theory. Automatica, 12(5), 457–465.

    Article  MathSciNet  MATH  Google Scholar 

  21. Huang, J. (2004). Nonlinear Output Regulation: Theory and Applications. Phildelphia, PA: SIAM.

    Book  MATH  Google Scholar 

  22. Khalil, H. K. (2002). Nonlinear Systems (3rd ed.). Upper Saddle River: Prentice Hall.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Automation, Xiamen University, Xiamen, 361005, Fujian, China

    Xinfei Wu, Xiao Yu & Weiyao Lan

  2. Key Laboratory of Control and Navigation (Xiamen University), Fujian Province University, Xiamen, 361005, Fujian, China

    Xiao Yu & Weiyao Lan

Authors
  1. Xinfei Wu
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  2. Xiao Yu
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  3. Weiyao Lan
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Corresponding author

Correspondence to Weiyao Lan.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grants 62273285 and 62173283, and in part by the Natural Science Foundation of Fujian Province of China under Grants 2021J01051.

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Wu, X., Yu, X. & Lan, W. Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator. Control Theory Technol. 21, 414–424 (2023). https://doi.org/10.1007/s11768-023-00167-6

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  • DOI: https://doi.org/10.1007/s11768-023-00167-6

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