Distributed Proportional–Integral Fuzzy State Estimation Over Sensor Networks Under Energy-Constrained Denial-of-Service Attacks

This article deals with the distributed proportional–integral state estimation problem for nonlinear systems over sensor networks (SNs), where a number of spatially distributed sensor nodes are utilized to collect the system information. The signal transmissions among different sensor nodes are realized via their individual channels subject to energy-constrained Denial-of-Service (EC-DoS) cyber-attacks launched by the adversaries whose aim is to block the nodewise communications. Such EC-DoS attacks are characterized by a sequence of attack starting time-instants and a sequence of attack durations. Based on the measurement outputs of each node, a novel distributed fuzzy proportional–integral estimator is proposed that reflects the topological information of the SNs. The estimation error dynamics is shown to be regulated by a switching system under certain assumptions on the frequency and the duration of the EC-DoS attacks. Then, by resorting to the average dwell-time method, a unified framework is established to analyze the dynamical behaviors of the resultant estimation error system, and sufficient conditions are obtained to guarantee the stability as well as the weighted
$H_{\infty }$
performance of the estimation error dynamics. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme.