access icon free Dynamic consensus of double-integrator multi-agent systems with aperiodic impulsive protocol and time-varying delays

© The Institution of Engineering and Technology
Received 24/12/2016, Accepted 03/08/2017, Revised 29/05/2017, Published 03/08/2017

This study involves an examination of the dynamic consensus problem for networks of double-integrator agents with aperiodic impulsive protocol and fixed topology. With respect to each agent, the control law is designed based on relative state measurements (i.e. position and velocity) between the agent and the neighbouring agents at a few discrete times. Additionally, these state measurements can include time-varying measurement delays. The theory of impulsive differential equations is used to prove that the dynamic consensus can be achieved under the condition of a graph with a spanning tree and to provide the consensus state finally reached by all agents. Furthermore, the study establishes algebraic inequalities that should be satisfied by the control gains, the bounds of impulsive interval lengths, and the upper bound of delays. Two numerical examples are illustrated to validate the main results.

Inspec keywords: directed graphs; control system synthesis; trees (mathematics); time-varying systems; differential equations; delays; discrete time systems; matrix algebra

Other keywords: impulsive differential equations; upper delay bound; impulsive interval length bounds; double-integrator multiagent systems; fixed topology; relative position state measurement; consensus state; dynamic consensus problem; control law design; control gains; time-varying measurement delays; relative velocity state measurement; graph condition; spanning tree; algebraic inequalities; aperiodic impulsive protocol

Subjects: Linear algebra (numerical analysis); Differential equations (numerical analysis); Control system analysis and synthesis methods; Time-varying control systems; Combinatorial mathematics; Distributed parameter control systems; Discrete control systems

References

    1. 1)
      • 20. Ren, W.: ‘Consensus strategies for cooperative control of vehicle formations’, IET Control Theory Appl., 2007, 1, (2), pp. 505–512.
    2. 2)
      • 25. Ren, W., Cao, Y.C.: ‘Convergence of sampled-data consensus algorithms for double-integrator dynamics’. Proc. 47th IEEE Conf. Decision and Control, Cancun, Mexico, December 2008, pp. 3965–3970.
    3. 3)
      • 5. Ren, W., Atkins, E.: ‘Distributed multi-vehicle coordinated control via local information exchange’, Int. J. Robust Nonlinear Control, 2007, 17, (10-11), pp. 1002–1033.
    4. 4)
      • 8. Jiang, F.C., Wang, L.: ‘Finite-time information consensus for multi-agent systems with fixed and switching topologies’, Physica D, 2009, 238, (16), pp. 1550–1560.
    5. 5)
      • 12. Zheng, Y.S., Wang, L.: ‘Consensus of switched multiagent systems’, IEEE Trans. Circuits Syst. II Express Briefs, 2016, 63, (3), pp. 314–318.
    6. 6)
      • 13. Zheng, Y.S., Ma, J.Y., Wang, L.: ‘Consensus of Hybrid Multi-agent Systems’, IEEE Trans. Neural Netw. Learn. Syst., 2017, Doi: 10.1109/TNNLS.2017.2651402.
    7. 7)
      • 6. Xie, G.M., Wang, L.: ‘Consensus control for a class of networks of dynamic agents’, Int. J. Robust Nonlinear Control, 2007, 17, (10-11), pp. 941–959.
    8. 8)
      • 19. Olfati-Saber, R., Fax, J.A., Murray, R.M.: ‘Consensus and cooperation in networked multi-agent systems’, Proc. IEEE, 2007, 95, (1), pp. 215–233.
    9. 9)
      • 10. Lin, X., Zheng, Y.S.: ‘Finite-Time consensus of switched multiagent systems’, IEEE Trans. Syst. Man Cybern. Syst., 2017, 47, (7), pp. 1535–1545.
    10. 10)
      • 15. Wu, Y.J., Wang, L.: ‘Sampled-data consensus for multi-agent systems with quantised communication’, Int. J. Control, 2015, 88, (2), pp. 413–428.
    11. 11)
      • 29. Liu, Z.W., Guan, Z.H., Shen, X., et al.: ‘Consensus of multi-agent networks with aperiodic sampled communication via impulsive algorithms using position-only measurements’, IEEE Trans. Autom. Control, 2012, 57, (10), pp. 2639–2643.
    12. 12)
      • 21. Su, H.S., Chen, M.Z.Q., Chen, G.R.: ‘Robust semi-global coordinated tracking of linear multi-agent systems with input saturation’, Int. J. Robust Nonlinear Control, 2015, 25, (14), pp. 2375–2390.
    13. 13)
      • 18. Ji, Z.J., Lin, H., Yu, H.S.: ‘Protocols design and uncontrollable topologies construction for multi-agent networks’, IEEE Trans. Autom. Control, 2015, 60, (3), pp. 781–786.
    14. 14)
      • 16. Xie, D.M., Liang, T.: ‘Second-order group consensus for multi-agent systems with time delays’, Neurocomputing, 2015, 153, pp. 133–139.
    15. 15)
      • 7. Xiao, L., Boyd, S.: ‘Fast linear iterations for distributed averaging’, Syst. Control Lett., 2004, 53, (1), pp. 65–78.
    16. 16)
      • 35. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, New York, 1985).
    17. 17)
      • 32. Wang, Y., Liu, M., Liu, Z., et al.: ‘Formation tracking of the second-order multi-agent systems using position-only information via impulsive control with input delays’, Appl. Math. Comput., 2014, 246, pp. 572–585.
    18. 18)
      • 30. Jiang, F.C., Xie, D.M., Liu, B.: ‘Static consensus of second-order multiagent systems with impulsive algorithm and time-delays’, Neurocomputing, 2017, 223, pp. 18–25.
    19. 19)
      • 34. Huang, L.: ‘Theoretical foundation of stability and robustness’ (Science Press, Beijing, 2003, (in Chinese)).
    20. 20)
      • 3. 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.
    21. 21)
      • 31. Zhang, H., Zhou, J.: ‘Distributed impulsive consensus for second-order multi-agent systems with input delays’, IET Control Theory Appl., 2013, 7, (16), pp. 1978–1983.
    22. 22)
      • 22. Su, H.S., Jia, G., Chen, M.Z.Q.: ‘Semi-global containment control of multi-agent systems with intermittent input saturation’, J. Frankl. Inst. Eng. Appl. Math., 2015, 352, (9), pp. 3504–3525.
    23. 23)
      • 26. Gao, Y.P., Wang, L.: ‘Sampled-data based consensus of continuous-time multi-agent systems with time-varying topology’, IEEE Trans. Autom. Control, 2011, 56, (5), pp. 1226–1231.
    24. 24)
      • 28. Guan, Z.H., Liu, Z.W., Feng, G., et al.: ‘Impulsive consensus algorithms for second-order multi-agent networks with sampled information’, Automatica, 2012, 48, (7), pp. 1397–1404.
    25. 25)
      • 11. Gao, Y.P., Ma, J.W., Zuo, M.: ‘Consensus of discrete-time second-order agents with time-varying topology and time-varying delays’, J. Frankl. Inst. Eng. Appl. Math., 2012, 349, (8), pp. 2598–2608.
    26. 26)
      • 17. Wang, L., Jiang, F.C., Xie, G.M., et al.: ‘Controllability of multi-agent systems based on agreement protocols’, Sci. China Ser. F Inf. Sci., 2009, 52, (11), pp. 2074–2088.
    27. 27)
      • 2. Jiang, F.C., Wang, L.: ‘Finite-time weighted average consensus with respect to a monotonic function and its application’, Syst. Control Lett., 2011, 60, (9), pp. 718–725.
    28. 28)
      • 23. Xie, G.M., Liu, H.Y., Wang, L., et al.: ‘Consensus in networked multi-agent systems via sampled control: fixed topology case’. 2009 Proc. American Control Conf., St. Louis, MO, US, June 2009, pp. 3902–3907.
    29. 29)
      • 24. Xie, G.M., Liu, H.Y., Wang, L., et al.: ‘Consensus in networked multi-agent systems via sampled control: switching topology case’. 2009 Proc. American Control Conf., St. Louis, MO, US, June 2009, pp. 4525–4530.
    30. 30)
      • 1. 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.
    31. 31)
      • 27. Xiao, F., Chen, T.W.: ‘Sampled-data consensus for multiple double integrators with arbitrary sampling’, IEEE Trans. Autom. Control, 2012, 57, (12), pp. 3230–3235.
    32. 32)
      • 14. Sun, W., Lü, J.H., Yu, X.H.: ‘Second-order consensus of multi-agent systems with noise’, IET Control Theory Appl., 2014, 8, (17), pp. 2026–2032.
    33. 33)
      • 4. Ren, W., Beard, R.W.: ‘Consensus seeking in multi-agent systems under dynamically changing interaction topologies’, IEEE Trans. Autom. Control, 2005, 50, (1), pp. 655–661.
    34. 34)
      • 9. Zheng, Y.S., Wang, L.: ‘Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements’, Syst. Control Lett., 2012, 61, (8), pp. 871–878.
    35. 35)
      • 33. Liu, B., Liu, T., Dou, C.: ‘Stability of discrete-time delayed impulsive linear systems with application to multi-tracking’, Int. J. Control, 2014, 87, (5), pp. 911–924.
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