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Zbl 1230.93089
Dong, Hongli; Lam, James; Gao, Huijun
Distributed $\cal H_{ \infty }$ filtering for repeated scalar nonlinear systems with random packet losses in sensor networks.
(English)
[J] Int. J. Syst. Sci. 42, No. 9, 1507-1519 (2011). ISSN 0020-7721; ISSN 1464-5319/e

Summary: This article is concerned with the distributed $\cal H_{\infty }$ filtering problem for sensor networks with repeated scalar nonlinearities and multiple probabilistic packet losses. The class of nonlinear systems is represented by a discrete-time state-space model involving repeated scalar nonlinearities that cover several types of frequently investigated nonlinearities as special cases. A number of stochastic variables, all of which are mutually independent but satisfy a certain probabilistic distribution in the interval [0, 1], are introduced to account for the packet dropout phenomena occurring in the channels from the original system to the networked sensors. The concept of average $\cal H_{\infty }$ index is first introduced to measure the overall performance of the sensor networks. Then, by utilizing available measurement information from not only each individual sensor but also its neighboring sensors according a given topology, stability analysis is carried out to obtain sufficient conditions for ensuring stochastic stability as well as the prescribed average $\cal H_{\infty }$ performance constraint. The solution of the parameters of the distributed filters is characterized in terms of the feasibility of a convex optimization problem. Finally, a simulation study is conducted for a factory production line in order to demonstrate the effectiveness of the developed theoretical results.
MSC 2000:
*93E11 Filtering in stochastic control
93B36 $H^\infty$-control
93C10 Nonlinear control systems
93C95 Appl. of control theory
90C25 Convex programming
93C55 Discrete-time control systems
93E15 Stochastic stability

Keywords: distributed filtering; $\cal H_\infty$ filtering; packet losses; repeated scalar nonlinearity; sensor networks

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