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Nonlinear Dynamics

, Volume 82, Issue 4, pp 2059–2068 | Cite as

Global coordinated tracking of multi-agent systems with disturbance uncertainties via bounded control inputs

  • Housheng Su
  • Michael Z. Q. Chen
  • Xiaofan Wang
Original Paper

Abstract

This paper investigates the problem of global coordinated tracking of a multi-agent system with input additive uncertainties and disturbances via bounded control inputs. Scheduled low-and-high gain feedback-based distributed coordinated tracking protocols are developed. It is shown that, under the assumptions that each agent is asymptotically null controllable with bounded controls and the network is connected, global coordinated tracking of the multi-agent system can be achieved. We finally show some numerical simulations to verify and illustrate the theoretical results.

Keywords

Coordinated tracking Multi-agent systems Disturbance uncertainties Low-and-high gain feedback 

References

  1. 1.
    Ren, W., Beard, R., Atkins, E.: Information consensus in multivehicle cooperative control: collective group behavior through local interaction. IEEE Control Syst. Mag. 27, 71–82 (2007)CrossRefGoogle Scholar
  2. 2.
    Chen, M., Wu, Q., Jiang, C.: Disturbance-observer-based robust synchronization control of uncertain chaotic systems. Nonlinear Dyn. 70, 2421–2432 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gholami, A., Markazi, A.: A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems. Nonlinear Dyn. 70, 2095–2105 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cheng, J., Zhu, H., Zhong, S., Zhong, Q., Zeng, Y.: Finite-time H-infinity estimation for discrete-time Markov jump systems with time-varying transition probabilities subject to average dwell time switching. Commun. Nonlinear Sci. Numer. Simul. 20, 571–582 (2015)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Cheng, J., Xiong, L., Wang, B., Yang, J.: Robust finite-time boundedness of H-infinity filtering for switched systems with time-varying delay. Optim. Control Appl. Methods (2015). doi: 10.1002/oca.2165
  6. 6.
    Wu, H., Wang, J.: Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics. Nonlinear Dyn. 72, 615–628 (2013)MATHCrossRefGoogle Scholar
  7. 7.
    Reynolds, C. W.: Flocks, herds, and schools: a distributed behavioral model. Comput. Graph. ACM SIGGRAPH 87 Conference Proceedings 21, 25–34 (1987)Google Scholar
  8. 8.
    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, O., Shochet, I.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)CrossRefGoogle Scholar
  9. 9.
    Su, H., Wang, X.: Pinning Control of Complex Networked Systems: Synchronization, Consensus and Flocking of Networked Systems via Pinning. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Cao, Y., Ren, W.: Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans. Autom. Control 57, 33–48 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hong, Y., Hu, J., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42, 1177–1182 (2006)MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Ren, W.: Multi-vehicle consensus with a time-varying reference state. Syst. Control Lett. 56, 474–483 (2007)MATHCrossRefGoogle Scholar
  13. 13.
    Shi, H., Wang, L., Chu, T.G.: Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions. Physica D 213, 51–65 (2006)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Yao, J., Ordonez, R., Gazi, V.: Swarm tracking using artificial potentials and sliding mode control. J. Dyn. Syst. Meas. Control 129, 749–754 (2007)CrossRefGoogle Scholar
  15. 15.
    Xie, G., Wang, L.: Consensus control for a class of networks of dynamic agents. Int. J. Robust Nonlinear Control 17, 941–959 (2007)MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Su, H., Wang, X., Lin, Z.: Flocking of multi-agents with a virtual leader. IEEE Trans. Autom. Control 54, 293–307 (2009)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Su, H., Wang, X., Chen, G.: Rendezvous of multiple mobile agents with preserved network connectivity. Syst. Control Lett. 59, 313–322 (2010)MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Li, Z., Duan, Z., Chen, G., Huang, L.: Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans. Circuits Syst. I: Regul. Pap. 57, 213–224 (2010)MathSciNetCrossRefGoogle Scholar
  19. 19.
    You, K., Xie, L.: Coordination of discrete-time multi-agent systems via relative output feedback. Int. J. Robust Nonlinear Control 21, 1587–1605 (2011)MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    You, K., Xie, L.: Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans. Autom. Control 56, 2262–2275 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Li, T., Fu, M., Xie, L., Zhang, J.: Distributed consensus with limited communication data rate. IEEE Trans. Autom. Control 56, 279–292 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yu, W., Chen, G., Cao, M., Kurths, J.: Second-order consensus for multi-agent systems with directed topologies and nonlinear dynamics. IEEE Trans. Syst. Man Cybern.-Part B 40, 881–891 (2010)CrossRefGoogle Scholar
  23. 23.
    Su, H., Chen, G., Wang, X., Lin, Z.: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47, 368–375 (2011)MATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Morales-Caporal, R., Pacas, M.: Suppression of saturation effects in a sensorless predictive controlled synchronous reluctance machine based on voltage space phasor injections. IEEE Trans. Ind. Electron. 58, 2809–2817 (2011)CrossRefGoogle Scholar
  25. 25.
    Maeda, Y., Wada, M., Iwasaki, M., Hirai, H.: Improvement of settling performance by mode-switching control with split initial-value compensation based on input shaper. IEEE Trans. Ind. Electron. 60, 979–987 (2013)Google Scholar
  26. 26.
    Cheng, L., Hou, Z., Tan, M., Lin, Y., Zhang, W.: Neural-network based adaptive leader-following control for multi-agent systems with uncertainties. IEEE Trans. Neural Netw. 21, 1351–1358 (2010)CrossRefGoogle Scholar
  27. 27.
    Wang, H., Xie, Y.: Prediction error based adaptive Jacobian tracking of robots with uncertain kinematics and dynamics. IEEE Trans. Autom. Control 54, 2889–2894 (2009)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Li, Y., Xiang, J., Wei, W.: Consensus problems for linear time-invariant multi-agent systems with saturation constraints. IET Control Theory Appl. 5, 823–829 (2011)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Ren, W.: On consensus algorithms for double-integrator dynamics. IEEE Trans. Autom. Control 53, 1503–1509 (2008)CrossRefGoogle Scholar
  30. 30.
    Liu, Z., Chen, Z.: Discarded consensus of network of agents with state constraint. IEEE Trans. Autom. Control 57, 2869–2874 (2012)CrossRefGoogle Scholar
  31. 31.
    Zheng, Y., Zhu, Y., Wang, L.: Consensus of heterogeneous multi-agent systems. IET Control Theory Appl. 5, 1881–1888 (2011)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Zheng, Y., Wang, L.: Consensus of heterogeneous multi-agent systems without velocity measurements. Int. J. Control 85, 906–914 (2012)MATHCrossRefGoogle Scholar
  33. 33.
    Su, H., Chen, M.Z.Q., Lam, J., Lin, Z.: Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback. IEEE Trans. Circuits Syst.-I: Regul. Pap. 60, 1881–1889 (2013)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Su, H., Chen, M.Z.Q., Wang, X., Lam, J.: Semiglobal observer-based leader-following consensus with input saturation. IEEE Trans. Ind. Electron. 61, 2842–2850 (2014)CrossRefGoogle Scholar
  35. 35.
    Su, H., Chen, M.Z.Q., Chen, G.: Robust semi-global coordinated tracking of linear multi-agent systems with input saturation. Int. J. Robust Nonlinear Control (2014). doi: 10.1002/rnc.3210
  36. 36.
    Lin, Z.: Low Gain Feedback. Lecture Notes in Control and Information Sciences. Springer, London (1998)Google Scholar
  37. 37.
    Godsil, C., Royle, G.: Algebraic Graph Theory. Graduate Texts in Mathematics. Springer, New York (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Housheng Su
    • 1
  • Michael Z. Q. Chen
    • 2
  • Xiaofan Wang
    • 3
  1. 1.School of Automation, Image Processing and Intelligent Control Key Laboratory of Education Ministry of ChinaHuazhong University of Science and TechnologyWuhanChina
  2. 2.Department of Mechanical EngineeringThe University of Hong KongPokfulamHong Kong
  3. 3.Department of AutomationShanghai Jiao Tong UniversityShanghaiChina

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