© The Institution of Engineering and Technology
This study involves an examination of the dynamic consensus problem for networks of doubleintegrator 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 timevarying 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.
References


1)

1. OlfatiSaber, R., Murray, R.M.: ‘Consensus problems in networks of agents with switching topology and timedelays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 1520–1533.

2)

2. Jiang, F.C., Wang, L.: ‘Finitetime weighted average consensus with respect to a monotonic function and its application’, Syst. Control Lett., 2011, 60, (9), pp. 718–725.

3)

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.

4)

4. Ren, W., Beard, R.W.: ‘Consensus seeking in multiagent systems under dynamically changing interaction topologies’, IEEE Trans. Autom. Control, 2005, 50, (1), pp. 655–661.

5)

5. Ren, W., Atkins, E.: ‘Distributed multivehicle coordinated control via local information exchange’, Int. J. Robust Nonlinear Control, 2007, 17, (1011), pp. 1002–1033.

6)

6. Xie, G.M., Wang, L.: ‘Consensus control for a class of networks of dynamic agents’, Int. J. Robust Nonlinear Control, 2007, 17, (1011), pp. 941–959.

7)

7. Xiao, L., Boyd, S.: ‘Fast linear iterations for distributed averaging’, Syst. Control Lett., 2004, 53, (1), pp. 65–78.

8)

8. Jiang, F.C., Wang, L.: ‘Finitetime information consensus for multiagent systems with fixed and switching topologies’, Physica D, 2009, 238, (16), pp. 1550–1560.

9)

9. Zheng, Y.S., Wang, L.: ‘Finitetime consensus of heterogeneous multiagent systems with and without velocity measurements’, Syst. Control Lett., 2012, 61, (8), pp. 871–878.

10)

10. Lin, X., Zheng, Y.S.: ‘FiniteTime consensus of switched multiagent systems’, IEEE Trans. Syst. Man Cybern. Syst., 2017, 47, (7), pp. 1535–1545.

11)

11. Gao, Y.P., Ma, J.W., Zuo, M.: ‘Consensus of discretetime secondorder agents with timevarying topology and timevarying delays’, J. Frankl. Inst. Eng. Appl. Math., 2012, 349, (8), pp. 2598–2608.

12)

12. Zheng, Y.S., Wang, L.: ‘Consensus of switched multiagent systems’, IEEE Trans. Circuits Syst. II Express Briefs, 2016, 63, (3), pp. 314–318.

13)

13. Zheng, Y.S., Ma, J.Y., Wang, L.: ‘Consensus of Hybrid Multiagent Systems’, IEEE Trans. Neural Netw. Learn. Syst., 2017, .

14)

14. Sun, W., Lü, J.H., Yu, X.H.: ‘Secondorder consensus of multiagent systems with noise’, IET Control Theory Appl., 2014, 8, (17), pp. 2026–2032.

15)

15. Wu, Y.J., Wang, L.: ‘Sampleddata consensus for multiagent systems with quantised communication’, Int. J. Control, 2015, 88, (2), pp. 413–428.

16)

16. Xie, D.M., Liang, T.: ‘Secondorder group consensus for multiagent systems with time delays’, Neurocomputing, 2015, 153, pp. 133–139.

17)

17. Wang, L., Jiang, F.C., Xie, G.M., et al.: ‘Controllability of multiagent systems based on agreement protocols’, Sci. China Ser. F Inf. Sci., 2009, 52, (11), pp. 2074–2088.

18)

18. Ji, Z.J., Lin, H., Yu, H.S.: ‘Protocols design and uncontrollable topologies construction for multiagent networks’, IEEE Trans. Autom. Control, 2015, 60, (3), pp. 781–786.

19)

19. OlfatiSaber, R., Fax, J.A., Murray, R.M.: ‘Consensus and cooperation in networked multiagent systems’, Proc. IEEE, 2007, 95, (1), pp. 215–233.

20)

20. Ren, W.: ‘Consensus strategies for cooperative control of vehicle formations’, IET Control Theory Appl., 2007, 1, (2), pp. 505–512.

21)

21. Su, H.S., Chen, M.Z.Q., Chen, G.R.: ‘Robust semiglobal coordinated tracking of linear multiagent systems with input saturation’, Int. J. Robust Nonlinear Control, 2015, 25, (14), pp. 2375–2390.

22)

22. Su, H.S., Jia, G., Chen, M.Z.Q.: ‘Semiglobal containment control of multiagent systems with intermittent input saturation’, J. Frankl. Inst. Eng. Appl. Math., 2015, 352, (9), pp. 3504–3525.

23)

23. Xie, G.M., Liu, H.Y., Wang, L., et al.: ‘Consensus in networked multiagent systems via sampled control: fixed topology case’. 2009 Proc. American Control Conf., St. Louis, MO, US, June 2009, pp. 3902–3907.

24)

24. Xie, G.M., Liu, H.Y., Wang, L., et al.: ‘Consensus in networked multiagent systems via sampled control: switching topology case’. 2009 Proc. American Control Conf., St. Louis, MO, US, June 2009, pp. 4525–4530.

25)

25. Ren, W., Cao, Y.C.: ‘Convergence of sampleddata consensus algorithms for doubleintegrator dynamics’. Proc. 47th IEEE Conf. Decision and Control, Cancun, Mexico, December 2008, pp. 3965–3970.

26)

26. Gao, Y.P., Wang, L.: ‘Sampleddata based consensus of continuoustime multiagent systems with timevarying topology’, IEEE Trans. Autom. Control, 2011, 56, (5), pp. 1226–1231.

27)

27. Xiao, F., Chen, T.W.: ‘Sampleddata consensus for multiple double integrators with arbitrary sampling’, IEEE Trans. Autom. Control, 2012, 57, (12), pp. 3230–3235.

28)

28. Guan, Z.H., Liu, Z.W., Feng, G., et al.: ‘Impulsive consensus algorithms for secondorder multiagent networks with sampled information’, Automatica, 2012, 48, (7), pp. 1397–1404.

29)

29. Liu, Z.W., Guan, Z.H., Shen, X., et al.: ‘Consensus of multiagent networks with aperiodic sampled communication via impulsive algorithms using positiononly measurements’, IEEE Trans. Autom. Control, 2012, 57, (10), pp. 2639–2643.

30)

30. Jiang, F.C., Xie, D.M., Liu, B.: ‘Static consensus of secondorder multiagent systems with impulsive algorithm and timedelays’, Neurocomputing, 2017, 223, pp. 18–25.

31)

31. Zhang, H., Zhou, J.: ‘Distributed impulsive consensus for secondorder multiagent systems with input delays’, IET Control Theory Appl., 2013, 7, (16), pp. 1978–1983.

32)

32. Wang, Y., Liu, M., Liu, Z., et al.: ‘Formation tracking of the secondorder multiagent systems using positiononly information via impulsive control with input delays’, Appl. Math. Comput., 2014, 246, pp. 572–585.

33)

33. Liu, B., Liu, T., Dou, C.: ‘Stability of discretetime delayed impulsive linear systems with application to multitracking’, Int. J. Control, 2014, 87, (5), pp. 911–924.

34)

34. Huang, L.: ‘Theoretical foundation of stability and robustness’ (Science Press, Beijing, 2003, (in Chinese)).

35)

35. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, New York, 1985).
http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta.2016.1515
Related content
content/journals/10.1049/ietcta.2016.1515
pub_keyword,iet_inspecKeyword,pub_concept
6
6