Kybernetika 51 no. 5, 814-829, 2015

Distributed H-infinity estimation for moving target under switching multi-agent network

Hu Chen, Qin Weiwei, He Bing and Liu GangDOI: 10.14736/kyb-2015-5-0814

Abstract:

In this paper, the distributed $H_\infty$ estimation problem is investigated for a moving target with local communication and switching topology. Based on the solution of the algebraic Riccati equation, a recursive algorithm is proposed using constant gain. The stability of the proposed algorithm is analysed by using the Lyapounov method, and a lower bound for estimation errors is obtained for the proposed common $H_\infty$ filter. Moreover, a bound for the $H_{\infty}$ parameter is obtained by means of the solution of the algebraic Riccati equation. Finally, a simulation example is employed to illustrate the effectiveness of the proposed estimation algorithm.

Keywords:

multi-agent systems, switching topology, distributed estimation, $H_\infty $ filter

Classification:

93E12, 62A10

paper.pdf

References:

  1. F. S. Cattivelli and A. H. Sayed: Diffusion LMS strategies for distributed estimation. IEEE Trans. Signal Process. 58 (2010), 1035-1048.   DOI:10.1109/tsp.2009.2033729
  2. F. S. Cattivelli and A. H. Sayed: Diffusion strategies for distributed Kalman filtering and smoothing. IEEE Trans. Automat. Control 55 (2010), 2069-2084.   DOI:10.1109/tac.2010.2042987
  3. H. Dong, Z. Wang and H. Gao: Distributed $H_\infty$ filtering for a class of Markovian jump nonlinear time-delay systems over Lossy sensor networks. IEEE Trans. Industr. Electronics 60 (2013), pp. 4665-4672.   DOI:10.1109/tie.2012.2213553
  4. C. Godsil and G. Royle: Algebraic Graph Theory. Springer-Verlag, New York 2001.   CrossRef
  5. Y. Hong, J. Hu and L. X. Gao: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42 (2006), 1177-1182.   DOI:10.1016/j.automatica.2006.02.013
  6. Y. Hong and X. Wang: Multi-agent tracking of a high-dementional active leader with switching topology. J. Systems Sci. Complex. 22 (2009), 722-731.   DOI:10.1007/s11424-009-9197-z
  7. R. A. Horn and C. R. Johnson: Matrix Analysis. Cambridge University Press, 2012.   CrossRef
  8. J. Hu, L. Xie and C. Zhang: Diffusion Kalman filtering based on covariance intersection. In: Proc. 18th IFAC World Congress, Milano 2011, pp. 12471-12476.   DOI:10.1007/s11424-009-9197-z
  9. T. Kailath, A. H. Sayed and B. Hassibi: Linear Estimation. Prentice Hall, New Jersey 2000.   CrossRef
  10. S. Kar and J. M. F. Moura: Grossip and distributed Kalman filtering: weak consensus under weak detectability. IEEE Trans. Signal Process. 59 (2011), 1766-1784.   DOI:10.1109/tsp.2010.2100385
  11. A. W. Marshall, I. Olkin and B. C. Arnold: Inequalities: Theory of Majorization and Its Applications. Springer-Verlag, New York 2010.   CrossRef
  12. T. R. Nelson and R. A. Freeman: Decentralized $H_\infty$ filtering in a multi-agent system. In: Proc. 2009 American Control Conference, St. Louis 2009, pp. 5755-5760.   DOI:10.1109/acc.2009.5160702
  13. A. Nemirovskii and P. Gahinet: The projective method for solving linear matrix inequalities. In: Proc. 1994 American Control Conference, Baltimore 1994, pp. 840-844.   DOI:10.1109/acc.1994.751861
  14. R. Olfati-Saber: Distributed Kalman filtering for sensor networks. In: Proc. 46th IEEE Conference on Decision and Control, New Orleans 2007, pp. 5492-5498.   DOI:10.1109/cdc.2007.4434303
  15. R. Olfati-Saber: Kalman-consensus filter : optimality, stability, and performance. In: Proc. 48th IEEE Conference on Decision and Control, Proc. 28th Chinese Control Conference, Shanghai 2009, pp. 7036-7042.   DOI:10.1109/cdc.2009.5399678
  16. R. Olfati-Saber and P. Jalalkamali: Collaborative target tracking using distributed Kalman filtering on mobile sensor networks. In: Proc. 2011 American Control Conference, San Francisco 2011, pp. 1100-1105.   DOI:10.1109/acc.2011.5990979
  17. H. Ramamurthy, B. S. Prabhu, R. Gadh and A. M. Madni: Wireless industrial monitoring and control using a smart sensor platform. IEEE Sensors J. 7 (2007), 611-618.   DOI:10.1109/jsen.2007.894135
  18. I. Saboori and K. Khorasani: $H_\infty$ consensus achievement of multi-agent systems with disrected and switching topology networks. IEEE Trans. Automat. Control 59 (2014), 3104-3109.   DOI:10.1109/tac.2014.2358071
  19. B. Shen, Z. Wang and Y. S. Hung: Distributed $H_\infty$-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case. Automatica 46 (2010), 1682-1688.   DOI:10.1016/j.automatica.2010.06.025
  20. V. Ugrinovskii: Distributed robust filtering with $H_\infty$ consensus of estimates. Automatica 47 (2011), 1-13.   DOI:10.1016/j.automatica.2010.10.002
  21. V. Ugrinovskii and E. Fridman: A Round-Robin type protocol for distributed estimation with $H_\infty$ consensus. Systems Control Lett. 69 (2014), 103-110.   DOI:10.1016/j.sysconle.2014.05.001
  22. Q. Zhang and J. Zhang: Distributed parameter estimation over unreliable networks with Markovian switching topologies. IEEE Trans. Automat. Control 57 (2012), 2545-2560.   DOI:10.1109/tac.2012.2188353
  23. Z. Zhou, H. Fang and Y. Hong: Distributed estimation for moving target under switching interconnection network. In: Proc. 12th International Conference on Control Automation Robotics Vision (ICARCV), Guangzhou 2012, pp. 1818-1823.   DOI:10.1109/icarcv.2012.6485302
  24. Z. Zhou, H. Fang and Y. Hong: Distributed estimation for moving target based on state-consensus strategy. IEEE Trans. Automat. Control 58 (2013), 2096-2101.   DOI:10.1109/tac.2013.2246476