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Optimal linear estimation for networked systems with communication constraints. (English) Zbl 1227.93117
Summary: This paper is concerned with the optimal linear estimation problem for discrete time-varying networked systems with communication constraints. The communication constraint considered is that only one network node is allowed to gain access to a shared communication channel, then the various network nodes of the networked systems are scheduled to transmit data according to a specified media access control protocol, and a remote estimator performs the estimation task with only partially available measurements. The channel accessing processes of those network nodes are modeled by Bernoulli processes, and optimal linear filters are designed by using the orthogonal projection principle and the innovation analysis approach. It is shown that the optimal estimation performances critically depend on the channel accessing probabilities of the network nodes and the packet loss probability, and the optimal filters can be obtained by solving recursive Lyapunov and Riccati equations. An illustrative example is finally given to show the effectiveness of the proposed filters.

##### MSC:
 93E10 Estimation and detection in stochastic control theory 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems
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##### References:
 [1] Dacic, D.; Nesic, D., Quadratic stabilization of linear networked control systems via simultaneous protocol and controller design, Automatica, 43, 7, 1145-1155, (2007) · Zbl 1123.93076 [2] Dacic, D.; Nesic, D., Observer design for wired linear networked control systems using matrix inequalities, Automatica, 44, 11, 2840-2849, (2008) · Zbl 1152.93314 [3] Dong, H.L.; Wang, Z.D.; Gao, H.J., Robust $$H_\infty$$ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts, IEEE transactions on signal processing, 58, 4, 1957-1966, (2010) · Zbl 1392.94183 [4] Gao, H.J.; Chen, T.W., $$H_\infty$$ estimation for uncertain systems with limited communication capacity, Transactions on automatic control, 52, 11, 2070-2084, (2007) · Zbl 1366.93155 [5] Garcia, A.L.; Widjaja, I., Communication networks: fundamental concepts and key architectures, (2001), McGraw-Hill [6] He, X.; Wang, Z.D.; Zhou, D., Robust $$H_\infty$$ filtering for networked systems with multiple state delays, International journal of control, 80, 8, 1217-1232, (2007) · Zbl 1133.93314 [7] Hounkpevi, F.O.; Yaz, E.E., Robust minimum variance linear state estimators for multiple sensors with different failure rates, Automatica, 43, 7, 1274-1280, (2007) · Zbl 1123.93085 [8] Hristu-Varsakelis, D., Short-period communication and the role of zero-order holding in networked control systems, Transactions on automatic control, 53, 5, 1285-1290, (2008) · Zbl 1367.93258 [9] Hristu-Varsakelis, D.; Morgansen, K., Limited communication control, Systems & control letters, 37, 4, 193-205, (1999) · Zbl 0948.93034 [10] Ishii, H., $$H_\infty$$ control with limited communication and message losses, Systems & control letters, 57, 4, 322-331, (2008) · Zbl 1133.93016 [11] Kailath, T.; Sayed, A.H.; Hassibi, B., Linear estimation, (2000), Prentice Hall [12] Liu, X. H., & Goldsmith, A. (2004). Kalman filtering with partial observation losses. In Proc. 43rd IEEE Conf. Decision and Control, Atlantls, USA. (pp. 4180-4186). [13] Lu, L. L., & Xie, L. H. (2003). Robust $$H_\infty$$ filtering for discrete-time systems with limited communication. In Proc. 4th International Conference on Control and Automation, Montreal, Canada. (pp. 737-741). [14] Mo, Y. L., Ambrosino, R., & Sinopoli, B. (2009). A convex optimization approach of multi-step sensor selection under correlated noise. In Proc. 47th Annual Allerton Conference on Communication, Control, and Computing, Illinoise, USA. (pp. 186-193). [15] Moayedi, M.; Foo, Y.K.; Soh, Y.C., Adaptive Kalman filtering in networked systems with random sensor delays, multiple packet dropouts and missing measurements, IEEE transactions on signal processing, 58, 3, 1577-1588, (2010) · Zbl 1391.93252 [16] Moshtagh, N., Chen, L. J., & Mehra, R. (2009). Optimal measurement selection for any-time kalman filtering with processing constraints. In Joint Proc. 48th IEEE Conf. Decision and Control and 28th Chinese Control Conf., Shanghai, PR China. (pp. 5074-5079). [17] Rehbinder, H.; Sanfridson, M., Scheduling of a limited communication channel for optimal control, Automatica, 40, 3, 491-500, (2004) · Zbl 1044.93040 [18] Sahebsara, M.; Chen, T.W.; Shah, S.L., Optimal $$H_2$$ filtering in networked control systems with multiple packet dropout, Transactions on automatic control, 52, 8, 1508-1513, (2007) · Zbl 1366.93659 [19] Schenato, L., Optimal estimation in networked control systems subject to random delay and packet drop, Transactions on automatic control, 53, 5, 1311-1317, (2008) · Zbl 1367.93633 [20] Schenato, L., To zero or to hold control inputs with lossy links?, Transactions on automatic control, 54, 5, 1093-1099, (2009) · Zbl 1367.93722 [21] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M.I.; Sastry, S.S., Kalman filtering with intermittent observations, Transactions on automatic control, 49, 9, 1453-1464, (2004) · Zbl 1365.93512 [22] Song, H.B.; Zhang, W.A.; Yu, L., $$H_\infty$$ filtering of network-based systems with communication constraints, IET signal processing, 4, 1, 55-68, (2010) [23] Sun, S.L.; Xie, L.H.; Xiao, W.D.; Soh, Y.C., Optimal linear estimation for systems with multiple packet dropouts, Automatica, 44, 7, 1333-1342, (2008) · Zbl 1283.93271 [24] Wang, Z.D.; Ho, D.W.C.; Liu, X.H., Variance-constrained filtering for uncertain stochastic systems with missing measurements, Transactions on automatic control, 48, 7, 1254-1258, (2003) · Zbl 1364.93814 [25] Wang, Z.D.; Yang, F.W.; Ho, D.W.C.; Liu, X.H., Robust finite-horizon filtering for stochastic systems with missing measurements, IEEE signal processing letters, 12, 6, 437-440, (2005) [26] Wu, D.; Wu, J.; Chen, S., Robust $$H_\infty$$ control for networked control systems with uncertainties and multiple-packet transmission, IET control theory and applications, 4, 5, 701-709, (2009) [27] Xiao, N.; Xie, L.; Fu, M., Kalman filtering over unreliable communication networks with bounded Markovian packet dropouts, International journal of robust and nonlinear control, 19, 16, 1770-1786, (2009) · Zbl 1298.93334 [28] Zeltwanger, H., An inside look at the fundamentals of CAN, Control engineering, 42, 1, 81-87, (1995) [29] Zhang, L.; Hristu-Varsakelis, D., Communication and control co-design for networked control systems, Automatica, 42, 6, 953-958, (2006) · Zbl 1117.93302
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