Distributed extended Kalman filtering for state-saturated nonlinear systems subject to randomly occurring cyberattacks w
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(2020) 2020:437
RESEARCH
Open Access
Distributed extended Kalman filtering for state-saturated nonlinear systems subject to randomly occurring cyberattacks with uncertain probabilities Jiaxing Li1 , Jun Hu1,3* , Dongyan Chen1,2 and Zhihui Wu1,3 *
Correspondence: [email protected] 1 Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China 3 School of Engineering, University of South Wales, Pontypridd CF37 1DL, UK Full list of author information is available at the end of the article
Abstract In this paper, the extended Kalman filtering scheme in a distributed manner is presented for state-saturated nonlinear systems (SSNSs), where the randomly occurring cyberattacks (ROCAs) with uncertain occurring probabilities (UOPs) are taken into account. In particular, a novel cyberattack model is constructed by the consideration of false data-injection attacks (FDIAs) and denial-of-service attacks (DoSAs) simultaneously. The ROCAs are described by a series of Bernoulli distributed stochastic variables, where the so-called UOPs are considered and described by the nominal mathematical expectations and error bounds. The major effort is to develop a novel DEKF strategy for SSNSs with consideration of state delay and ROCAs with UOPs. In what follows, an upper bound with respect to the filtering error covariance is derived and minimized by selecting the suitable filter parameter. Besides, the concrete expression of the filter parameter is formed by solving matrix difference equations (MDEs). Meanwhile, a sufficient condition under certain constraints is proposed to testify the boundedness regarding the given upper bound. Finally, we use the experiments and corresponding comparisons to verify the feasibility of the designed extended Kalman filtering approach in a distributed way. Keywords: Distributed extended Kalman filtering; State-saturated systems; Time delay; Uncertain occurring probabilities; Randomly occurring cyberattacks
1 Introduction During the past few decades, the dynamical networks have been extensively applied to the modeling in a wealth of areas such as air cooperative monitoring, seismic sensing, target tracking and so forth, see, e.g., [1–6] for more details. Accordingly, a wireless sensor network (WSN) comprises a majority of intelligent nodes, which are capable of sensing, monitoring, collecting data information, and communicating with their adjacent nodes at the same time. In order to reduce production costs, each intelligent node normally has small size and limited power in practical engineering systems. Thus, the traditional filtering method, which requires that every node transmits the information to the fusion center or other sensor nodes, has certain application limitations [7, 8]. To handle this issue, the © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and t
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