Distributed ℋ_∞ filtering for repeated scalar nonlinear systems with random packet losses in sensor networks

Abstract

This article is concerned with the distributed ℋ_∞ 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_∞ index is first introduced to measure the overall performance of the sensor networks. Then, by utilising available measurement information from not only each individual sensor but also its neighbouring 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_∞ performance constraint. The solution of the parameters of the distributed filters is characterised in terms of the feasibility of a convex optimisation problem. Finally, a simulation study is conducted for a factory production line in order to demonstrate the effectiveness of the developed theoretical results.

Keywords:

• distributed filtering
• ℋ_∞ filtering
• packet losses
• repeated scalar nonlinearity
• sensor networks

Acknowledgements

This work was supported in part by the University of Hong Kong under Grant No. HKU/CRCG/200907176129, the National Natural Science Foundation of China under Grant No. 60834003 and 61004067 and the Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No. 2007B4.