http://iet.metastore.ingenta.com
1887

Consensus for second-order agent dynamics with velocity estimators via pinning control

Consensus for second-order agent dynamics with velocity estimators via pinning control

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

A consensus problem is investigated for a group of second-order agents with an active leader where the velocity of the leader cannot be measured, and the leader as well as all the agents is governed by the same non-linear intrinsic dynamics. To achieve consensus in the sense of both position and velocity, a neighbour-based estimator design approach and a pinning-controlled algorithm are proposed for each autonomous agent. It is found that all the agents in the group can follow the leader, and the velocity tracking errors of estimators converge to zero asymptotically, without assuming that the interaction topology is strongly connected or contains a directed spanning tree. In terms of the switching topologies between the leader and the followers, similar results are obtained. Finally, these theoretical results are demonstrated by the numerical simulations.

References

    1. 1)
      • 1. Watts, D.J., Strogatz, S.H.: ‘Collective dynamics of small-world networks’, Nature, 1998, 393, (6), pp. 440442 (doi: 10.1038/30918).
    2. 2)
      • 2. Liang, J., Shen, B., Dong, H., James, L.: ‘Robust distributed state estimation for sensor networks with multiple stochastic communication delays’, Int. J. Syst. Sci., 2011, 42, (9), pp. 14591471 (doi: 10.1080/00207721.2010.550402).
    3. 3)
      • 3. Ren, W., Atkins, E.M.: ‘Distributed multi-vehicle coordinated control via local information exchange’, Int. J. Robust Nonlinear Control, 2007, 17, (10), pp. 10021033 (doi: 10.1002/rnc.1147).
    4. 4)
      • 4. Liu, H., Xie, G., Wang, L.: ‘Containment of linear multi-agent systems under general interaction topologies’, Syst. Control Lett., 2012, 61, (4), pp. 528534 (doi: 10.1016/j.sysconle.2012.01.012).
    5. 5)
      • 5. Cao, Y., Yu, W., Ren, W., Chen, G.: ‘An overview of recent progress in the study of distributed multi-agent coordination’, IEEE Trans. Ind. Inf., 2013, 9, (1), pp. 427438 (doi: 10.1109/TII.2012.2219061).
    6. 6)
      • 6. Liang, J., Wang, Z., Liu, X., Louvieris, P.: ‘Robust synchronization for 2-D discrete-time coupled dynamical networks’, IEEE Trans. Neural Netw. Learn. Syst., 2012, 23, (6), pp. 942953 (doi: 10.1109/TNNLS.2012.2193414).
    7. 7)
      • 7. Xiao, F., Wang, L.: ‘Asynchronous rendezvous analysis via set-valued consensus theory’, SIAM J. Control Optim., 2012, 50, (1), pp. 196221 (doi: 10.1137/100801202).
    8. 8)
      • 8. Yu, W., Lü, J., Wang, Z., Cao, J., Zhou, Q.: ‘Robust H-infinite control and uniformly bounded control for genetic regulatory network with stochastic disturbance’, IET Control Theory Appl., 2010, 4, (9), pp. 16871706 (doi: 10.1049/iet-cta.2010.0003).
    9. 9)
      • 9. Yu, W., Chen, G., Cao, M.: ‘Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems’, Automatica, 2010, 46, (6), pp. 10891095 (doi: 10.1016/j.automatica.2010.03.006).
    10. 10)
      • 10. Qin, J., Zheng, W.X., Gao, H.: ‘Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology’, Automatica, 2011, 47, (9), pp. 19831991 (doi: 10.1016/j.automatica.2011.05.014).
    11. 11)
      • 11. Xie, G., Wang, L.: ‘Consensus control for a class of networks of dynamic agents’, Int. J. Robust Nonlinear Control, 2007, 17, (10), pp. 941959 (doi: 10.1002/rnc.1144).
    12. 12)
      • 12. Zheng, Y., Zhu, Y., Wang, L.: ‘Consensus of heterogeneous multi-agent systems’, IET Control Theory Appl., 2011, 5, (16), pp. 18811888 (doi: 10.1049/iet-cta.2011.0033).
    13. 13)
      • 13. Wen, G., Duan, Z., Yu, W., Chen, G.: ‘Consensus in multi-agent systems with communication constraints’, Int. J. Robust Nonlinear Control, 2012, 22, (2), pp. 170182 (doi: 10.1002/rnc.1687).
    14. 14)
      • 14. Yu, W., Chen, G., Cao, M.: ‘Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities’, Syst. Control Lett., 2010, 59, (9), pp. 543552 (doi: 10.1016/j.sysconle.2010.06.014).
    15. 15)
      • 15. Shao, J., Xie, G., Wang, L.: ‘Leader-following formation control of multiple mobile vehicles’, IET Control Theory Appl., 2007, 1, (2), pp. 545552 (doi: 10.1049/iet-cta:20050371).
    16. 16)
      • 16. Su, H., Wang, X., Lin, Z.: ‘Flocking of multi-agents with a virtual leader’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 293307 (doi: 10.1109/TAC.2008.2010897).
    17. 17)
      • 17. Song, Q., Cao, J., Yu, W.: ‘Second-order leader-following consensus of nonlinear multi-agent systems via pinning control’, Syst. Control Lett., 2010, 59, (9), pp. 553562 (doi: 10.1016/j.sysconle.2010.06.016).
    18. 18)
      • 18. Grigoriev, R.O., Cross, M.C., Schuster, H.G.: ‘Pinning control of spatiotemporal chaos’, Phys. Rev. Lett., 1997, 79, (15), pp. 27952798 (doi: 10.1103/PhysRevLett.79.2795).
    19. 19)
      • 19. Parekh, N., Parthasarathy, S., Sinha, S.: ‘Global and local control of spatiotemporal chaos in coupled map lattices’, Phys. Rev. Lett., 1998, 81, (7), pp. 14011404 (doi: 10.1103/PhysRevLett.81.1401).
    20. 20)
      • 20. Wang, X., Chen, G.: ‘Pinning control of scale-free dynamical networks’, Physica A, 2002, 310, (3), pp. 521531 (doi: 10.1016/S0378-4371(02)00772-0).
    21. 21)
      • 21. Yu, W., Chen, G., Lü, J.: ‘On pinning synchronization of complex dynamical networks’, Automatica, 2009, 45, (2), pp. 429435 (doi: 10.1016/j.automatica.2008.07.016).
    22. 22)
      • 22. Qin, J., Zheng, W.X., Gao, H.: ‘On pinning synchronisability of complex networks with arbitrary topological structure’, Int. J. Syst. Sci., 2011, 42, (9), pp. 15591571 (doi: 10.1080/00207721.2011.555014).
    23. 23)
      • 23. Hong, Y., Hu, J., Gao, L.: ‘Tracking control for multi-agent consensus with an active leader and variable topology’, Automatica, 2006, 42, (7), pp. 11771182 (doi: 10.1016/j.automatica.2006.02.013).
    24. 24)
      • 24. Peng, K., Yang, Y.: ‘Leader-following consensus problem with a varying-velocity leader and time-varying delays’, Physica A, 2009, 388, (2), pp. 193208 (doi: 10.1016/j.physa.2008.10.009).
    25. 25)
      • 25. Godsil, C., Royle, G.: ‘Algebraic graph theory’ (Springer, New York, 2001).
    26. 26)
      • 26. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, 1994).
    27. 27)
      • 27. Huang, L.: ‘Linear algebra in systems and control theory’ (Science Press, Beijing, China, 1984).
    28. 28)
      • 28. Song, Q., Cao, J.: ‘On pinning synchronization of directed and undirected complex dynamical networks’, IEEE Trans. Circuits Syst. I, 2010, 57, (3), pp. 672680 (doi: 10.1109/TCSI.2009.2024971).
    29. 29)
      • 29. 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. B, Cybern., 2010, 40, (3), pp. 881891 (doi: 10.1109/TSMCB.2009.2031624).
    30. 30)
      • 30. Su, H., Chen, G., Wang, X., Lin, Z.: ‘Adaptive second-order consensus of networked mobile agents with nonlinear dynamics’, Automatica, 2011, 47, (2), pp. 368375 (doi: 10.1016/j.automatica.2010.10.050).
    31. 31)
      • 31. Liu, B., Hill, D.J.: ‘Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays’, SIAM J. Control Optim., 2011, 49, (2), pp. 315338 (doi: 10.1137/080722060).
    32. 32)
      • 32. Liberzon, D., Morse, A.S.: ‘Basic problems in stability and design of switched systems’, IEEE Contr. Syst. Mag., 1999, 19, (1), pp. 5970 (doi: 10.1109/37.793443).
    33. 33)
      • 33. Branicky, M.S.: ‘Multiple Lyapunov functions and other analysis tools for switched and hybrid systems’, IEEE Trans. Autom. Control, 1998, 43, (4), pp. 475482 (doi: 10.1109/9.664150).
    34. 34)
      • 34. Yu, W., Cao, J., Lü, J.: ‘Global synchronization of linearly hybrid coupled networks with time-varying delay’, SIAM J. Appl. Dyn. Syst., 2008, 7, (1), pp. 108133 (doi: 10.1137/070679090).
    35. 35)
      • 35. Lu, W., Li, X., Rong, Z.: ‘Global stabilization of complex networks with diagraph topologies via a local pinning algorithm’, Automatica, 2010, 46, (1), pp. 116121 (doi: 10.1016/j.automatica.2009.10.006).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0009
Loading

Related content

content/journals/10.1049/iet-cta.2013.0009
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address