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

Robust guaranteed cost consensus for high-order discrete-time multi-agent systems with parameter uncertainties and time-varying delays

Robust guaranteed cost consensus for high-order discrete-time multi-agent systems with parameter uncertainties and time-varying delays

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.

The robust guaranteed cost consensus problem of high-order discrete-time linear multi-agent systems (MASs) with parameter uncertainties and time-varying delays is studied, and a linear consensus protocol of it is designed. Norm-bounded uncertainties and polytopic uncertainties are considered. First, the idea of robust guaranteed cost control is introduced into consensus problems for the MASs, where a cost function is defined based on state errors among neighbouring agents and control inputs of all the agents. Second, by constructing suitable Lyapunov functions and using the stability theory of discrete-time linear systems, two sufficient linear matrix inequality conditions are derived to insure that high-order discrete-time linear MASs with the two types of parameter uncertainties and time-varying delays reach robust guaranteed cost consensus. At the same time, two upper bounds of the guaranteed cost function are also given. Third, convergence results are given as final consensus values of the MASs with parameter uncertainties and time-varying delays. Finally, two numerical comparisons are given to illustrate the correctness and availability of the theoretical results.

References

    1. 1)
      • 1. Kang, W., Yeh, H.H.: ‘Coordinated attitude control of multi-satellite systems’, Int. J. Robust Nonlinear Control, 2002, 12, (2), pp. 185205.
    2. 2)
      • 2. Godard, K.D., Kumar, K.D.: ‘Fault tolerant reconfigurable satellite formations using adaptive variable structure techniques’, J. Guid. Control Dyn., 2010, 33, (3), pp. 969984.
    3. 3)
      • 3. Abdessameud, A., Tayebi, A.: ‘Formation control of VTOL unmanned aerial vehicles with communication delays’, Automatica, 2011, 47, (11), pp. 23832394.
    4. 4)
      • 4. Wang, J., Xin, M.: ‘Integrated optimal formation control of multiple unmanned aerial vehicles’, IEEE Trans. Control Syst. Tech., 2013, 21, (5), pp. 17311744.
    5. 5)
      • 5. Kar, S., Moura, J.M.F.: ‘Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise’, IEEE Trans. Signal Proc., 2009, 57, (1), pp. 355369.
    6. 6)
      • 6. Kibangou, A.Y.: ‘Step-size sequence design for finite-time average consensus in secure wireless sensor networks’, Syst. Control Lett., 2014, 67, (7), pp. 1923.
    7. 7)
      • 7. 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. 15201533.
    8. 8)
      • 8. Xiao, F., Wang, L.: ‘Consensus problems for high-dimensional multi-agent systems’, IET Control Theory Appl., 2007, 1, (3), pp. 830837.
    9. 9)
      • 9. Xi, J., Cai, N., Zhong, Y.: ‘Consensus problems for high-order linear time-invariant swarm systems’, Physica A, 2010, 389, (24), pp. 56195627.
    10. 10)
      • 10. Xi, J., Shi, Z., Zhong, Y.: ‘Output consensus analysis and design for high-order linear swarm systems: partial stability method’, Automatica, 2012, 48, (5), pp. 23352343.
    11. 11)
      • 11. You, K., Xie, L.: ‘Network topology and communication data rate for consensusability of discrete-time multi-agent systems’, IEEE Trans. Autom. Control, 2011, 56, (10), pp. 22622275.
    12. 12)
      • 12. Su, Y., Huang, J.: ‘Two consensus problems for discrete-time multi-agent systems with switching network topology’, Automatica, 2012, 48, (9), pp. 19881997.
    13. 13)
      • 13. Zhao, H., Park, J., Zhang, Y., et al: ‘Distributed output feedback consensus of discrete-time multi-agent systems’, Neurocomputing, 2014, 138, (9), pp. 8691.
    14. 14)
      • 14. He, W., Cao, J.: ‘Consensus control for high order multi-agent systems’, IET Control Theory Appl., 2011, 5, (1), pp. 231238.
    15. 15)
      • 15. Xin, Y., Cheng, Z.: ‘r-consensus control for discrete-time high-order multi-agent systems’, IET Control Theory Appl., 2013, 7, (17), pp. 21032109.
    16. 16)
      • 16. Xin, Y., Cheng, Z.: ‘r-consensus control for high-order multi-agent systems with digraph’, Asian J. Control , 2013, 15, (5), pp. 15241530.
    17. 17)
      • 17. Guan, Z., Hu, B., Chi, M., et al: ‘Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control’, Automatica, 2014, 50, pp. 24152418.
    18. 18)
      • 18. Wang, Z., Xi, J., Yao, Z., et al: ‘Guaranteed cost consensus for multi-agent systems with fixed topologies’, Asian J. Control , 2015, 17, (2), pp. 729735.
    19. 19)
      • 19. Wang, Z., Xi, J., Yao, Z., et al: ‘Guaranteed cost consensus problems for second-order multi-agent systems’, IET Control Theory Appl., 2015, 9, (3), pp. 367373.
    20. 20)
      • 20. Cheng, Y., Ugrinovskii, V.: ‘Guaranteed performance leader-follower control for multiagent systems with linear IQC-constrained coupling’. Proc. American Control Conf., 2013, pp. 26252630.
    21. 21)
      • 21. Xie, C.H., Yang, G.H.: ‘Cooperative guaranteed cost fault-tolerant control for multi-agent systems with time-varying actuator faults’, Neurocomputing, 2016.
    22. 22)
      • 22. Xu, J., Zhang, G., Zeng, J., et al: ‘Robust guaranteed cost consensus for high-order discrete-time multi-agent systems with directed graphs’. Proc. The 35th Chinese Control Conf., 2016, pp. 75387545.
    23. 23)
      • 23. Terra, H., Cerri, P., Ishihara, Y.: ‘Optimal robust linear quadratic regulator for systems subject to uncertainties’, IEEE Trans. Autom. Control, 2014, 59, (9), pp. 25862591.
    24. 24)
      • 24. Ian Petersen, R., Tempo, R.: ‘Robust control of uncertain systems: classical results and recent developments’, Automatica, 2014, 50, (2), pp. 13151335.
    25. 25)
      • 25. Chesi, G., Garulli, A., Tesi, A., et al: ‘Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach’, IEEE Trans. Autom. Control, 2005, 50, (3), pp. 365370.
    26. 26)
      • 26. Chesi, G.: ‘On the non-conservatism of a novel LMI relaxation for robust analysis of polytopic systems’, Automatica, 2008, 44, (11), pp. 29732976.
    27. 27)
      • 27. Fax, J.A., Murray, R.M.: ‘Information flow and cooperative control of vehicle formations’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 14651476.
    28. 28)
      • 28. Wu, M., He, Y., She, J.H., et al: ‘Delay-dependent criteria f or robust stability of time-varying delay systems’, Automatica, 2004, 40, pp. 14351439.
    29. 29)
      • 29. Wang, Y., Xie, L., Souza de, C.E.: ‘Robust control of a class of uncertain nonlinear systems’, Syst. Control Lett., 1992, 19, (3), pp. 139149.
    30. 30)
      • 30. Ghaoui, L., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
    31. 31)
      • 31. El Ghaoui, L., Oustry, F., AitRami, M.: ‘A cone complementarity linearization algorithm for static output-feedback and related problems’, IEEE Trans. Autom. Control, 1997, 42, (8), pp. 11711176.
    32. 32)
      • 32. Zhang, G., Xu, J., Zeng, J., et al: ‘Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays’, Trans. Inst. Meas. Control, 2016, pp. 113.
    33. 33)
      • 33. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, 1999).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.1214
Loading

Related content

content/journals/10.1049/iet-cta.2016.1214
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address