access icon free Containment control of second-order discrete-time multi-agent systems with Markovian missing data

© The Institution of Engineering and Technology
Received 24/04/2014, Accepted 15/10/2014, Published 08/04/2015

This study investigates the containment control problem of second-order discrete-time multi-agent systems with Markovian missing data in actuators and one step network-induced time delay. The process of missing data from the controller to the actuator is modelled by a homogeneous, finite-state and discrete-time Markov chain. The authors first discuss the containment control problem for the case when all the elements of the transition probability matrix are completely known, then the result is extended to a more general case with only partially known transition probabilities. The distributed control protocol with one step time delay is proposed. Based on the stochastic Lyapunov–Krasovskii functional method, sufficient conditions in terms of a set of matrix inequalities are given to guarantee that the states of all the followers asymptotically converge to the convex hull formed by the corresponding states of the leaders in mean square sense. A cone complementary linearisation algorithm is used to obtain the control gains. Finally, two numerical simulations are provided to show the effectiveness of theoretical results.

Inspec keywords: Markov processes; multi-agent systems; distributed control; matrix algebra; Lyapunov methods; delays; probability; discrete time systems; stochastic systems

Other keywords: containment control problem; partially known transition probabilities; distributed control protocol; sufficient conditions; finite-state Markov chain; second-order discrete-time multiagent systems; one step network-induced time delay; matrix inequalities; homogeneous Markov chain; Markovian missing data; actuators; stochastic Lyapunov–Krasovskii functional method; discrete-time Markov chain; transition probability matrix; cone complementary linearisation algorithm

Subjects: Algebra; Discrete control systems; Stability in control theory; Markov processes; Time-varying control systems; Distributed parameter control systems

References

    1. 1)
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
    7. 7)
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
      • 36. Zhang, X., Wu, M.: ‘Delay-dependent H∞ control for linear discrete-time uncertain systems with multiple unknown delays’, Control Theory Appl., 2006, 23, (6), pp. 918–922.
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
    18. 18)
    19. 19)
    20. 20)
    21. 21)
    22. 22)
    23. 23)
    24. 24)
    25. 25)
      • 35. Boyd, B., Ghaoui, L.E., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, PA, 1994).
    26. 26)
    27. 27)
      • 24. Mei, J., Ren, W., Ma, G.: ‘Distributed containment control for multiple nonlinear systems with identical dynamics’. Proc. 30th Chinese Control Conf., Yantai, China, July 2011, pp. 6544–6549.
    28. 28)
    29. 29)
      • 3. Lin, J., Morse, A.S., Anderson, B.D.O.: ‘The multi-agent rendezvous problem’. Proc. 42nd IEEE Conf. on Decision and Control, Hawaii, USA, December 2003, pp. 1508-1513.
    30. 30)
    31. 31)
    32. 32)
    33. 33)
    34. 34)
      • 5. Olfati-Saber, R., Shanma, J.S.: ‘Consensus filters for sensor networks and distributed sensor fusion’. Proc. 44th IEEE Conf. on Decision and Control, and the European Control Conf., Seville, Spain, December 2005, pp. 6698–6703.
    35. 35)
      • 33. Rockafellar, R.T.: ‘Convex analysis’ (Princeton University Press, New Jersey, 1972).
    36. 36)
    37. 37)
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2014.0895
Loading

Related content

content/journals/10.1049/iet-cta.2014.0895
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading