# Article

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Keywords:
multi-agent systems; distributed estimation; $H_\infty$ filter; switching topology
Summary:
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.
References:
[1] Cattivelli, F. S., Sayed, A. H.: Diffusion LMS strategies for distributed estimation. IEEE Trans. Signal Process. 58 (2010), 1035-1048. DOI 10.1109/tsp.2009.2033729 | MR 2751419
[2] Cattivelli, F. S., Sayed, A. H.: Diffusion strategies for distributed Kalman filtering and smoothing. IEEE Trans. Automat. Control 55 (2010), 2069-2084. DOI 10.1109/tac.2010.2042987 | MR 2722500
[3] Dong, H., Wang, Z., Gao, H.: 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] Godsil, C., Royle, G.: Algebraic Graph Theory. Springer-Verlag, New York 2001. MR 1829620 | Zbl 0968.05002
[5] Hong, Y., Hu, J., Gao, L. X.: 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 | MR 2230987 | Zbl 1117.93300
[6] Hong, Y., Wang, X.: 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 | MR 2565265
[7] Horn, R. A., Johnson, C. R.: Matrix Analysis. Cambridge University Press, 2012. Zbl 0801.15001
[8] Hu, J., Xie, L., Zhang, C.: 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 | MR 2919485
[9] Kailath, T., Sayed, A. H., Hassibi, B.: Linear Estimation. Prentice Hall, New Jersey 2000. Zbl 0862.93056
[10] Kar, S., Moura, J. M. F.: Grossip and distributed Kalman filtering: weak consensus under weak detectability. IEEE Trans. Signal Process. 59 (2011), 1766-1784. DOI 10.1109/tsp.2010.2100385 | MR 2807748
[11] Marshall, A. W., Olkin, I., Arnold, B. C.: Inequalities: Theory of Majorization and Its Applications. Springer-Verlag, New York 2010. MR 2759813 | Zbl 1219.26003
[12] Nelson, T. R., Freeman, R. A.: 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] Nemirovskii, A., Gahinet, P.: 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] Olfati-Saber, R.: 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] Olfati-Saber, R.: 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] Olfati-Saber, R., Jalalkamali, P.: 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] Ramamurthy, H., Prabhu, B. S., Gadh, R., Madni, A. M.: Wireless industrial monitoring and control using a smart sensor platform. IEEE Sensors J. 7 (2007), 611-618. DOI 10.1109/jsen.2007.894135
[18] Saboori, I., Khorasani, K.: $H_\infty$ 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 | MR 3271167
[19] Shen, B., Wang, Z., Hung, Y. S.: 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 | MR 2877323 | Zbl 1204.93122
[20] Ugrinovskii, V.: Distributed robust filtering with $H_\infty$ consensus of estimates. Automatica 47 (2011), 1-13. DOI 10.1016/j.automatica.2010.10.002 | MR 2878241 | Zbl 1209.93152
[21] Ugrinovskii, V., Fridman, E.: 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 | MR 3212828 | Zbl 1288.93009
[22] Zhang, Q., Zhang, J.: Distributed parameter estimation over unreliable networks with Markovian switching topologies. IEEE Trans. Automat. Control 57 (2012), 2545-2560. DOI 10.1109/tac.2012.2188353 | MR 2991656
[23] Zhou, Z., Fang, H., Hong, Y.: 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] Zhou, Z., Fang, H., Hong, Y.: Distributed estimation for moving target based on state-consensus strategy. IEEE Trans. Automat. Control 58 (2013), 2096-2101. DOI 10.1109/tac.2013.2246476 | MR 3090041

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