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Distributed ${ℋ}_{\infty }$ filtering for repeated scalar nonlinear systems with random packet losses in sensor networks. (English) Zbl 1230.93089
Summary: This article is concerned with the distributed ${ℋ}_{\infty }$ 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 ${ℋ}_{\infty }$ 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 ${ℋ}_{\infty }$ 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:
 93E11 Filtering in stochastic control 93B36 ${H}^{\infty }$-control 93C10 Nonlinear control systems 93C95 Applications of control theory 90C25 Convex programming 93C55 Discrete-time control systems 93E15 Stochastic stability