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Zbl 1244.93162
Wang, Zidong; Shen, Bo; Liu, Xiaohui
$H_{\infty }$ filtering with randomly occurring sensor saturations and missing measurements.
(English)
[J] Automatica 48, No. 3, 556-562 (2012). ISSN 0005-1098

Summary: In this paper, the $H_{\infty }$ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, Randomly Occurring Sensor Saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional $H_{\infty }$ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the $H_{\infty }$-norm requirement is satisfied. Note that the regional $l_{2}$ gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semidefinite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.
MSC 2000:
*93E11 Filtering in stochastic control
93B36 $H^\infty$-control
93C55 Discrete-time control systems
93C10 Nonlinear control systems
90C22 Semidefinite programming

Keywords: randomly occurring sensor saturations (ROSS); missing measurements; nonlinear systems; regional $H_{\infty }$ filters; random incomplete information

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