Circuits, Systems, and Signal Processing

, Volume 38, Issue 5, pp 1982–1999 | Cite as

Robust Semiglobal Coordination of Coupled Harmonic Oscillator Systems Subject to Input Saturation

  • Feng Ni
  • Yaping SunEmail author
  • Minghui Yu
  • Xiangzhao Huang


In this paper, we investigate the problems of robust semiglobal coordination of coupled harmonic oscillator systems with input saturation together with dead zone and input additive disturbances, in which the coupled harmonic oscillators can serve as an approximation of modern complex systems in the field of system engineering, such as SoS (system of systems). By virtue of the parameterized low-and-high-gain feedback technique, sufficient conditions are provided to guarantee the robust semiglobal coordination of coupled harmonic oscillator systems with input saturation together with decentralized state-dependent input additive disturbances and distributed state-dependent input additive disturbances. Finally, numerical examples are proposed to verify all the theoretical results.


Coupled harmonic oscillators system SoS Coordination Input disturbance Dead zone Low-and-high-gain feedback 



This work was supported by the National Natural Science Foundation of China under Grant No. 61403255 and the National Defense Science foundation project of China under Grant No. JCKY 2017207B005.


  1. 1.
    X. Chen, M. Shi, H. Sun, Y. Li, H. He, Distributed cooperative control and stability analysis of multiple DC electric springs in a DC microgrid. IEEE Trans. Ind. Electron. 65(7), 5611–5622 (2018)CrossRefGoogle Scholar
  2. 2.
    X. Chen, Y. Hou, S.Y.R. Hui, Distributed control of multiple electric springs for voltage control in microgrid. IEEE Trans. Smart Grid 8(3), 1350–1359 (2017)CrossRefGoogle Scholar
  3. 3.
    M.Z.Q. Chen, L. Zhang, H. Su, G. Chen, Stabilizing solution and parameter dependence of modified algebraic riccati equation with application to discrete-time network synchronization. IEEE Trans. Automat. Control 61(1), 228–233 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Y. Jiang, J. Liu, S. Wang, Consensus tracking algorithm via observer-based distributed output feedback for multi-agent systems under switching topology. Circuits Syst. Signal Process. 33(10), 3037–3052 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Y. Lu, L. Zhang, X. Mao, Distributed information consensus filters for simultaneous input and state estimation. Circuits Syst. Signal Process. 32(2), 877–888 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Y. Liu, J. Slotine, A. Barabsi, Controllability of complex networks. Nature 473(7346), 167–73 (2011)CrossRefGoogle Scholar
  7. 7.
    A. Okubo, Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Adv. Biophys. 22(22), 1–94 (1986)CrossRefGoogle Scholar
  8. 8.
    R. Olfati-Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    R. Olfati-Saber, Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51(3), 401–420 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    H. Pan, W. Sun, H. Gao, J. Yu, Finite-time stabilization for vehicle active suspension systems with hard constraints. IEEE Trans. Intell. Transp. Syst. 16(5), 2663–2672 (2015)CrossRefGoogle Scholar
  11. 11.
    H. Pan, W. Sun, H. Gao, X. Jing, Disturbance observer-based adaptive tracking control with actuator saturation and its application. IEEE Trans. Autom. Sci. Eng. 13(2), 868–875 (2016)CrossRefGoogle Scholar
  12. 12.
    H. Pan, X. Jing, W. Sun, H. Gao, A bioinspired dynamics-based adaptive tracking control for nonlinear suspension systems IEEE Trans. Control Syst. Technol. (26)3, 903–914 (2018)Google Scholar
  13. 13.
    H. Su, H. Wu, X. Chen, M.Z.Q. Chen, Positive edge consensus of complex networks. IEEE Trans. Syst. Man Cybern. Syst. (2017)
  14. 14.
    H. Su, H. Wu, X. Chen, Observer-based discrete-time nonnegative edge synchronization of networked systems. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2446–2455 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    H. Su, M.Z.Q. Chen, J. Lam, Z. Lin, Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback. IEEE Trans. Circuits I 60(7), 1881–1889 (2013)MathSciNetGoogle Scholar
  16. 16.
    Q. Song, F. Liu, H. Su, A.V. Vasilakos, Semi-global and global containment control of multiagent systems with second-order dynamics and input saturation. Int. J. Robust Nonlinear 26(16), 3460–3480 (2016)CrossRefzbMATHGoogle Scholar
  17. 17.
    H. Su, Y. Qiu, L. Wang, Semi-global output consensus of discrete-time multi-agent systems with input saturation and external disturbances. ISA Trans. 67, 131–139 (2017)CrossRefGoogle Scholar
  18. 18.
    H. Su, M.Z.Q. Chen, X. Wang, J. Lam, Semiglobal observer-based leader-following consensus with input saturation. IEEE Trans. Ind. Electron. 61(6), 2842–2850 (2014)CrossRefGoogle Scholar
  19. 19.
    H. Su, M.Z.Q. Chen, G. Chen, Robust semi-global coordinated tracking of linear multiagent systems with input saturation. Int. J. Robust Nonlinear 25(14), 2375–2390 (2015)CrossRefzbMATHGoogle Scholar
  20. 20.
    J. Toner, Y. Tu, Hydrodynamics and phases of flocks. Ann. Phys. 318(1), 170–244 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    X. Wang, H. Su, X. Wang, B. Liu, Second-order consensus of multi-agent systems via periodically intermittent pinning control. Circuits Syst. Signal Process. 35(7), 2413–2431 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    X. Wang, X. Wang, H. Su, G. Chen, Fully distributed event-triggered consensus of multi-agent systems with input saturation. IEEE Trans. Ind. Electron. 64(6), 5055–5064 (2017)CrossRefGoogle Scholar
  23. 23.
    H. Wu, H. Su, Discrete-time positive edge-consensus for undirected and directed nodal networks. IEEE Trans. Circuits Syst. II: Express Briefs 65(2), 221–225 (2018)CrossRefGoogle Scholar
  24. 24.
    X. Wang, X. Wang, Semi-global consensus of multi-agent systems with intermittent communications and low-gain feedback. IET Control Theory A 9(5), 766–774 (2015)MathSciNetCrossRefGoogle Scholar
  25. 25.
    X.L. Wang, H. Su, M.Z.Q. Chen, X.F. Wang, Observer-based robust coordinated control of multiagent systems with input saturation. IEEE Trans. Neural Netw. Learn. 29(5), 1933–1946 (2018)MathSciNetCrossRefGoogle Scholar
  26. 26.
    X.L. Wang, H. Su, X.F. Wang, G. Chen, Robust semiglobal swarm tracking of coupled harmonic oscillators with input saturation and external disturbance. Int. J. Robust Nonlinear 28, 1566–1582 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Z. Zhao, Z. Lin, Semi-global leader-following consensus of multiple linear systems with position and rate limited actuators. Int. J. Robust Nonlinear 25(13), 2083–2100 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    B. Zhou, X. Liao, T. Huang, H. Li, G. Chen, Event-based semiglobal consensus of homogenous linear multi-agent systems subject to input saturation. Asian J. Control 19(2), 564–574 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Z. Zhang, Z. Zuo, Y. Wang, Finite-time consensus of neutrally stable multi-agent systems in the presence of input saturation. J. Franklin Inst. (2017)

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Feng Ni
    • 1
  • Yaping Sun
    • 2
    Email author
  • Minghui Yu
    • 2
  • Xiangzhao Huang
    • 3
  1. 1.Business SchoolUniversity of Shanghai for Science and TechnologyShanghaiPeople’s Republic of China
  2. 2.School of AutomationHuazhong University of Science and TechnologyWuhanPeople’s Republic of China
  3. 3.China Ship Development and Design CenterWuhanPeople’s Republic of China

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