Distributed Proportional–Integral Fuzzy State Estimation Over Sensor Networks Under Energy-Constrained Denial-of-Service Attacks
针对传感器网络中能量受限的拒绝服务攻击，提出一种分布式模糊比例积分估计器，利用切换系统理论分析估计误差的稳定性，并给出保证加权H∞性能的条件。
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> performance of the estimation error dynamics. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme.