This study investigates the distributed containment control for second-order multi-agent systems with multiple stationary or dynamic leaders based on only position information. Based on stability and algebraic graph theories, some necessary and sufficient conditions are obtained. Firstly, when the leaders are stationary, a necessary and sufficient condition is given to guarantee that all followers will ultimately converge to the stationary convex hull spanned by the stationary leaders for arbitrary initial states. The containment control protocol is designed based on a distributed filter, which is used for estimating the neighbours’ velocities of each follower. Secondly, when each leader is dynamic with constant velocity, using sampled current and outdated position data, a necessary and sufficient condition is obtained to drive the followers into the dynamic convex hull spanned by the dynamic leaders. Finally, some numerical simulations are presented to illustrate the proposed theories.

References

1. 1)
  - W. Ren , R.W. Beard . Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control , 5 , 655 - 661
2. 2)
  - Y. Hong , J. Hu , L. Gao . Tracking control for multi-agent consensus with an active leader and variable topology. Automatica , 7 , 1177 - 1182
3. 3)
  - R. Olfati-Saber , J.A. Fax , R.M. Murray . Consensus and cooperation in networked multi-agent systems. Proc. IEEE. , 1 , 215 - 233
4. 4)
  - 25. Li, J., Ren, W., Xu, S.: ‘Distributed containment control with multiple dynamic leaders for double-integrator dynamics using only position measurements’, IEEE Trans. Autom. Control, 2012, 57, (6), pp. 1553–1559 (doi: 10.1109/TAC.2011.2174680).
5. 5)
  - A. Jadbabaie , J. Lin , A.S. Morse . Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control , 6 , 988 - 1001
6. 6)
  - 20. Zheng, Y., Wang, L.: ‘Consensus of heterogeneous multi-agent systems without velocity measurements’, Int. J. Control, 2012, 85, (7), pp. 906–914 (doi: 10.1080/00207179.2012.669048).
7. 7)
  - Z. Meng , W. Ren , Z. You . Distributed finite-time attitude containment control for multiple rigid bodies. Automatica , 12 , 2092 - 2099
8. 8)
  - 30. Zheng, Y.S., Wang, L.: ‘Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements’, Syst. Control Lett., 2012, 61, pp. 871–878 (doi: 10.1016/j.sysconle.2012.05.009).
9. 9)
  - Z.J. Tang , T.Z. Huang , J.L. Shao , J.P. Hu . Leader-following consensus for multi-agent systems via sampled-data control. IET Control Theory Appl. , 14 , 1658 - 1665
10. 10)
  - 4. Ding, L., Yu, P., Liu, Z.W., Guan, Z.H.: ‘Consensus and performance optimisation of multi-agent systems with position-only information via impulsive control’, IET Control Theory Appl., 2013, 7, (1), pp. 16–24 (doi: 10.1049/iet-cta.2012.0461).
11. 11)
  - Z. Li , Z. Duran , G. Chen . Dynamic consensus of linear multi-agent systems. IET Control Theory Appl. , 1 , 19 - 28
12. 12)
  - 21. Liu, H.Y., Xie, G.M., Wang, L.: ‘Necessary and sufficient conditions for containment control of networked multi-agent systems’, Automatica, 2012, 48, (7), pp. 1415–1422 (doi: 10.1016/j.automatica.2012.05.010).
13. 13)
  - 20. Cao, Y.C., Stuart, D., Ren, W., Meng, Z.Y.: ‘Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithm and experiments’, IEEE Trans. Control Syst. Technol., 2011, 19, (4), pp. 929–938 (doi: 10.1109/TCST.2010.2053542).
14. 14)
  - J.A. Fax , R.M. Murray . Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control , 9 , 1465 - 1476
15. 15)
  - 17. Ji, M., Ferrari-Trecate, G., Egerstedt, M., Buffa, A.: ‘Containment control in mobile networks’, IEEE Trans. Autom. Control, 2008, 53, (8), pp. 1972–1975 (doi: 10.1109/TAC.2008.930098).
16. 16)
  - D.V. Dimarogonas , K.J. Kyriakopoulos . On the rendezvous problem for multiple nonholonomic agents. IEEE Trans. Autom. Control , 5 , 916 - 922
17. 17)
  - H. Su , X. Wang , G. Chen . Rendezvous of multiple mobile agents with preserved network connectivity. Syst. Control Lett. , 313 - 322
18. 18)
  - R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control , 9 , 1520 - 1533
19. 19)
  - 22. Li, Z.K., Ren, W., Liu, X.D., Fu, M.Y.: ‘Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders’, Int. J. Robust Nonlinear Control, 2013, 23, (5), pp. 534–547 (doi: 10.1002/rnc.1847).
20. 20)
  - H. Su , X. Wang , Z. Lin . Flocking of multi-agents with a virtual leader. IEEE Trans. Autom. Control , 293 - 307
21. 21)
  - 19. Cao, Y.C., Ren, W., Egerstedt, M.: ‘Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks’, Automatica, 2012, 48, (8), pp. 1586–1597 (doi: 10.1016/j.automatica.2012.05.071).
22. 22)
  - 16. Zhang, Y.J., Yang, Y., Zhao, Y., Wen, G.H.: ‘Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances’, Int. J. control, 2013, 86, (1), pp. 29–40 (doi: 10.1080/00207179.2012.717722).
23. 23)
  - 33. Gantmakher, F.R.: ‘The theory of matrices’ Chelsea Pub Co, New York, 2000.
24. 24)
  - 19. Lu, X.Q., Lu, R.Q., Chen, S.H., Lv, J.H.: ‘Finite-time distributed tracking control for multi-agent systems with a virtual leader’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2013, 60, (2), pp. 352–361 (doi: 10.1109/TCSI.2012.2215786).
25. 25)
  - R. Olfati-Saber . Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control , 3 , 401 - 420
26. 26)
  - P. Lin , Y. Jia . Robust H∞ consensus analysis of a class of second-order multi-agent systems with uncertainty. IET Control Theory Appl. , 3 , 487 - 498
27. 27)
  - Z. Lin , B.A. Francis , M. Maggiore . Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans. Autom. Control , 121 - 127
28. 28)
  - 7. 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. 427–438 (doi: 10.1109/TII.2012.2219061).
29. 29)
  - G. Wen , Z. Duan , H. Su , G. Chen , W. Yu . A connectivity-preserving flocking algorithm for multi-agent dynamical systems with bounded potential function. IET Control Theory Appl. , 6 , 813 - 821
30. 30)
  - H. Su , G. Chen , X. Wang , Z. Lin . Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica , 2 , 368 - 375
31. 31)
  - Y. Hong , G. Chen , L. Bushnell . Distributed observers design for leader-following control of multi-agent networks. Automatica , 3 , 846 - 850
32. 32)
  - H. Su , X. Wang , G. Chen . A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements. Int. J. Control , 7 , 1334 - 1343
33. 33)
  - 18. Liu, H., Xie, G., Wang, L.: ‘Containment of linear multi-agent systems under general interaction topologies’, Syst. Control Lett., 2012, 61, (4), pp. 528–534 (doi: 10.1016/j.sysconle.2012.01.012).

Necessary and sufficient conditions for distributed containment control of multi-agent systems without velocity measurement

References

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