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1887

access icon free Consensus of second-order multi-agents with actuator saturation and asynchronous time-delays

© The Institution of Engineering and Technology
Received 31/05/2017, Accepted 04/09/2017, Revised 21/08/2017, Published 04/09/2017

This study presents the consensus of a saturated second-order multi-agent system with non-switching dynamics that can be represented by a directed graph. The system is affected by data processing (input delay) and communication time-delays that are assumed to be asynchronous. The agents have saturation non-linearities, each of them is approximated into separate linear and non-linear elements. Non-linear elements are represented by describing functions. Describing functions and stability of linear elements are used to estimate the existence of limit cycles in the system with multiple control laws. Stability analysis of the linear element is performed using Lyapunov–Krasovskii functions and frequency domain analysis. A comparison of pros and cons of both the analyses with respect to time-delay ranges, applicability and computation complexity is presented. Simulation and corresponding hardware implementation results are demonstrated to support theoretical results.

Inspec keywords: frequency-domain analysis; delays; control nonlinearities; stability; Lyapunov methods; approximation theory; computational complexity; directed graphs; multi-robot systems; mobile robots

Other keywords: applicability complexity; saturated second-order multiagent system; asynchronous time-delays; multiple control laws; stability analysis; communication time-delays; data processing; linear elements; nonswitching dynamics; saturation nonlinearities; actuator saturation; frequency domain analysis; computation complexity; limit cycles; Lyapunov-Krasovskii functions; nonlinear elements; directed graph; input delay; time-delay ranges

Subjects: Nonlinear control systems; Mobile robots; Distributed parameter control systems; Computational complexity; Interpolation and function approximation (numerical analysis); Combinatorial mathematics; Stability in control theory

References

    1. 1)
      • 3. Vicsek, T., Czirók, A., Ben-Jacob, E., et al.: ‘Novel type of phase transition in a system of self-driven particles’, Phys. Rev. Lett., 1995, 75, pp. 1226–1229.
    2. 2)
      • 10. Meng, Z., Ren, W., Cao, Y., et al.: ‘Leaderless and leader–following consensus with communication and input delays under a directed network topology’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2011, 41, (1), pp. 75–88.
    3. 3)
      • 22. You, X., Hua, C., Peng, D., et al.: ‘Leader following consensus for multi-agent systems subject to actuator saturation with switching topologies and time-varying delays’, IET Control Theory Appl., 2016, 10, (2), pp. 144–150.
    4. 4)
      • 7. Ren, W.: ‘On consensus algorithms for double-integrator dynamics’, IEEE Trans. Autom. Control, 2008, 53, (6), pp. 1503–1509.
    5. 5)
      • 12. Meng, X., Meng, Z., Chen, T., et al.: ‘Pulse width modulation for multi-agent systems’, Automatica, 2016, 70, pp. 173–178.
    6. 6)
      • 11. Zhang, W., Liu, J., Zeng, D., et al.: ‘Consensus analysis of continuous-time second-order multi-agent systems with nonuniform time-delays and switching topologies’, Asian J. Control, 2013, 15, (5), pp. 1516–1523.
    7. 7)
      • 17. Meng, Z., Zhao, Z., Lin, Z.: ‘On global leader-following consensus of identical linear dynamic systems subject to actuator saturation’, Syst. Control Lett., 2013, 62, (2), pp. 132–142.
    8. 8)
      • 14. Liu, K., Xie, G., Ren, W., et al.: ‘Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies’, Syst. Control Lett., 2013, 62, (2), pp. 152–162.
    9. 9)
      • 2. Olfati-Saber, R., Murray, R.M.: ‘Consensus problems in networks of agents with switching topology and time-delays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 1520–1533.
    10. 10)
      • 13. Yu, W., Chen, G., Cao, M., et al.: ‘Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2010, 40, (3), pp. 881–891.
    11. 11)
      • 27. Sturm, J.F.: ‘Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones’, in ‘Optimization Methods and Software’, vol. 11-12, 1999, pp. 625–653.Version 1.05 available from http://fewcal.kub.nl/sturm.
    12. 12)
      • 9. Münz, U., Papachristodoulou, A., Allgöwer, F.: ‘Delay robustness in consensus problems’, Automatica, 2010, 46, (8), pp. 1252–1265.
    13. 13)
      • 18. Wei, A., Hu, X., Wang, Y.: ‘Tracking control of leader-follower multi-agent systems subject to actuator saturation’, IEEE/CAA J. Autom. Sin., 2014, 1, (1), pp. 84–91.
    14. 14)
      • 5. Wang, X., Zeng, Z., Cong, Y.: ‘Multi-agent distributed coordination control: developments and directions via graph viewpoint’, Neurocomputing, 2016, 199, pp. 204–218.
    15. 15)
      • 26. Lin, P., Jia, Y.: ‘Average consensus in networks of multi-agents with both switching topology and coupling time-delay’, Physica A, Stat. Mech. Appl., 2008, 387, (1), pp. 303–313.
    16. 16)
      • 24. Lin, P., Jia, Y.: ‘Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies’, IEEE Trans. Autom. Control, 2010, 55, (3), pp. 778–784.
    17. 17)
      • 1. Jadbabaie, A., Lin, J., Morse, A.S.: ‘Coordination of groups of mobile autonomous agents using nearest neighbor rules’, IEEE Trans. Autom. Control, 2003, 48, (6), pp. 988–1001.
    18. 18)
      • 20. Su, H., Chen, M.Z.Q.: ‘Multi-agent containment control with input saturation on switching topologies’, IET Control Theory Appl., 2015, 9, (3), pp. 399–409.
    19. 19)
      • 25. Slotine, J.J.E., Li, W.: ‘Describing function analysis’, ‘Applied nonlinear control’ (Englewood Cliffs, Prentice Hall, N.J., 1991), pp. 157–190.
    20. 20)
      • 4. Cao, Y., Yu, W., Ren, W., et al.: ‘An overview of recent progress in the study of distributed multi-agent coordination’, IEEE Trans. Ind. Inf., 2013, 9, (1), pp. 427–438.
    21. 21)
      • 19. Chu, H., Yuan, J., Zhang, W.: ‘Observer-based adaptive consensus tracking for linear multi-agent systems with input saturation’, IET Control Theory Appl., 2015, 9, (14), pp. 2124–2131.
    22. 22)
      • 15. Li, J., Guan, Z.H., Chen, G.: ‘Multi-consensus of nonlinearly networked multi-agent systems’, Asian J. Control, 2015, 17, (1), pp. 157–164.
    23. 23)
      • 8. Hu, J., Lin, Y.S.: ‘Consensus control for multi-agent systems with double-integrator dynamics and time delays’, IET Control Theory Appl., 2010, 4, (1), pp. 109–118.
    24. 24)
      • 16. Li, Y., Xiang, J., Wei, W.: ‘Consensus problems for linear time-invariant multi-agent systems with saturation constraints’, IET Control Theory Appl., 2011, 5, (6), pp. 823–829.
    25. 25)
      • 23. Sun, Y.G., Wang, L., Xie, G.: ‘Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays’, Syst. Control Lett., 2008, 57, (2), pp. 175–183.
    26. 26)
      • 21. Cui, G., Xu, S., Lewis, F.L., et al.: ‘Distributed consensus tracking for non-linear multi-agent systems with input saturation: a command filtered backstepping approach’, IET Control Theory Appl., 2016, 10, (5), pp. 509–516.
    27. 27)
      • 6. Xiao, F., Wang, L.: ‘Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays’, IEEE Trans. Autom. Control, 2008, 53, (8), pp. 1804–1816.
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