Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer

Wenhai Chen; Lixin Gao; Xiaole Xu; Bingbing Xu

Kybernetika (2015)

  • Volume: 51, Issue: 4, page 639-654
  • ISSN: 0023-5954

Abstract

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In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.

How to cite

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Chen, Wenhai, et al. "Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer." Kybernetika 51.4 (2015): 639-654. <http://eudml.org/doc/271797>.

@article{Chen2015,
abstract = {In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.},
author = {Chen, Wenhai, Gao, Lixin, Xu, Xiaole, Xu, Bingbing},
journal = {Kybernetika},
keywords = {multi-agent system; discrete-time system; distributed control; consensus; observer; multi-agent system; discrete-time system; distributed control; consensus; observer},
language = {eng},
number = {4},
pages = {639-654},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer},
url = {http://eudml.org/doc/271797},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Chen, Wenhai
AU - Gao, Lixin
AU - Xu, Xiaole
AU - Xu, Bingbing
TI - Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 4
SP - 639
EP - 654
AB - In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.
LA - eng
KW - multi-agent system; discrete-time system; distributed control; consensus; observer; multi-agent system; discrete-time system; distributed control; consensus; observer
UR - http://eudml.org/doc/271797
ER -

References

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  1. Cao, Y., Yu, W., Ren, W., Chen, G., 10.1109/tii.2012.2219061, IEEE Trans. Industr. Informatics 9 (2013), 427-4384. DOI10.1109/tii.2012.2219061
  2. Chen, C. T., Linear System Theory and Design. Third edition., Oxford University Press, New York 1999. 
  3. Franceschetti, M., Poolla, K., Jordan, M., Sastry, S., 10.1109/tac.2004.834121, IEEE Trans. Automat. Control 49 (2004), 1453-1464. MR2086911DOI10.1109/tac.2004.834121
  4. Gao, L., Tang, Y., Chen, W., Zhang, H., Consensus seeking in multi-agent systems with an active leader and communication delays., Kybernetika 47 (2011), 773-789. Zbl1236.93006MR2850463
  5. Gao, L., Tong, C., Wang, L., 10.1007/s13369-013-0807-7, The Arabian J. Sci. Engrg. 39 (2014), 1477-1487. MR3158186DOI10.1007/s13369-013-0807-7
  6. Gao, Y., Wang, L., 10.1049/iet-cta.2008.0565, IET Control Theory Appl. 4 (2010), 945-956. MR2680775DOI10.1049/iet-cta.2008.0565
  7. Gao, L., Xu, B., Li, J., Zhang, H., 10.1049/iet-cta.2013.1104, IET Control Theory Appl. 9 (2015), 784-792. MR3363254DOI10.1049/iet-cta.2013.1104
  8. Gao, L., Zhu, X., Chen, W., 10.1007/s12555-012-0509-z, Int. J. Control, Automation, and Systems 10 (2012), 5, 931-939. DOI10.1007/s12555-012-0509-z
  9. Hengster-Movric, K., Lewis, F., 10.1002/rnc.2840, Int. J. Robust and Nonlinear Control 23 (2013), 1545-1562. Zbl1286.93039MR3086126DOI10.1002/rnc.2840
  10. Hengster-Movric, K., You, K., Lewis, F. L., Xie, L., 10.1016/j.automatica.2012.11.038, Automatica 49 (2013), 414-423. Zbl1259.93005MR3004706DOI10.1016/j.automatica.2012.11.038
  11. Hong, Y., Hu, J., Gao, L., 10.1016/j.automatica.2006.02.013, Automatica 42 (2006), 1177-1182. Zbl1117.93300MR2230987DOI10.1016/j.automatica.2006.02.013
  12. Hong, Y., Chen, G., Bushnell, L., 10.1016/j.automatica.2007.07.004, Automatica 44 (2008), 846-850. MR2527101DOI10.1016/j.automatica.2007.07.004
  13. Hong, Y., Wang, X., 10.1007/s11424-009-9197-z, J. Systems Science Complex. 22 (2009), 722-731. Zbl1300.93014MR2565265DOI10.1007/s11424-009-9197-z
  14. Hu, J., Geng, J., Zhou, H., 10.1016/j.cnsns.2014.06.002, Comm. Nonlinear Sci. Numer. Simul. 20 (2015), 559-570. MR3251515DOI10.1016/j.cnsns.2014.06.002
  15. Hu, J., Zheng, W., 10.1016/j.automatica.2014.02.037, Automatica 50 (2014), 1416-1423. Zbl1296.93085MR3198780DOI10.1016/j.automatica.2014.02.037
  16. Jadbabaie, A., Lin, J., Morse, A. S., 10.1109/tac.2003.812781, IEEE Trans. Automat. Control 48 (2003), 988-1001. MR1986266DOI10.1109/tac.2003.812781
  17. Ke, Y., Xie, L., 10.1109/tac.2011.2164017, IEEE Trans. Automat. Control 56 (2011), 2262-2275. MR2884153DOI10.1109/tac.2011.2164017
  18. Li, Z., Duan, Z., Chen, G., Huang, L., 10.1109/tcsi.2009.2023937, IEEE Trans. on Circuits and Systems I: Regular Papers 57 (2010), 213-224. MR2729823DOI10.1109/tcsi.2009.2023937
  19. Li, Z., Liu, X., Lin, P., Ren, W., 10.1016/j.sysconle.2011.04.008, Systems Control Lett. 60 (2011), 510-516. Zbl1222.93013MR2849495DOI10.1016/j.sysconle.2011.04.008
  20. Liu, Y., Ho, D. W. C., Wang, Z., 10.1080/00207179.2012.703331, Int. J. Control 85 (2012), 1755-1765. Zbl1253.93081MR2980250DOI10.1080/00207179.2012.703331
  21. Olfati-Saber, R., Murrary, R. M., 10.1109/tac.2004.834113, IEEE Trans. Automat. Control. 49 (2004), 1520-1533. MR2086916DOI10.1109/tac.2004.834113
  22. Ren, W., Cao, Y., 10.1007/978-0-85729-169-1, Springer-Verlag London Limited 2011. Zbl1225.93003DOI10.1007/978-0-85729-169-1
  23. Su, Y., Huang, J., 10.1016/j.automatica.2012.03.029, Automatica 48 (2012), 1988-1997. Zbl1258.93015MR2956875DOI10.1016/j.automatica.2012.03.029
  24. Xu, B., Gao, L., Zhang, Y., Xu, X., 10.1155/2013/357971, Abstract and Applied Analysis 2013 (2013), 1-10. Zbl1291.93018MR3111802DOI10.1155/2013/357971
  25. Xu, B., Li, J., Gao, L., 10.3182/20130902-3-cn-3020.00040, In: Proc. 3rd IFAC International Conference on Intelligent Control and Automation Science, 2013, pp. 124-129. DOI10.3182/20130902-3-cn-3020.00040
  26. Xu, X., Chen, S., Huang, W., Gao, L., 10.1016/j.neucom.2013.02.023, Neurocomputing 118 (2013), 334-341. DOI10.1016/j.neucom.2013.02.023
  27. Xu, X., Chen, S., Gao, L., 10.1016/j.neucom.2014.12.037, Neurocomputing 156 (2015), 297-305. DOI10.1016/j.neucom.2014.12.037
  28. Zhai, C., Sweep coverage of discrete time multi-robot networks with general topologies., Kybernetika 50 (2014), 19-31. Zbl1302.93225MR3195002
  29. Zhang, H., Lewis, F. L., Das, A., 10.1109/tac.2011.2139510, IEEE Trans. Automat. Control 56 (2011), 1948-1952. MR2856813DOI10.1109/tac.2011.2139510

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