Distributed Set-Membership Filtering for Nonlinear Systems Subject to Stochastic Communication Protocol over Sensor Networks

A distributed set-membership filtering algorithm is proposed for a class of nonlinear system with sensor networks with the stochastic communication protocol (SCP). The system in this paper is subject to unknown but bounded noises and a kind of nonlinearity linearized via Taylor expansion formula. Via using the SCP technology, any node in the sensor network could receive information from only one of its neighbor nodes randomly at each moment. Other neighbor nodes intending to communicate with the node need to wait for a random interval till the channel is free for the waiting node. By means of recursive linear matrix inequalities (RLMIs), sufficient conditions are established for the existence of the desired filter parameters to guarantee the state estimate contained in the certain ellipsoidal region. Then an optimization problem minimizing the ellipsoids (in the sense of matrix trace) is raised up to improve the performance of the filter. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering algorithm.