Distributed extended Kalman filtering for state-saturated nonlinear systems subject to randomly occurring cyberattacks with uncertain probabilities

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 26
• Main Authors: Li, Jiaxing, Hu, Jun, Chen, Dongyan, Wu, Zhihui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 25.08.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Covariance; Denial of service attacks; Difference and Functional Equations; Difference equations; Distributed extended Kalman filtering; Functional Analysis; Kalman filters; Mathematics; Mathematics and Statistics; Matrix methods; Nonlinear systems; Ordinary Differential Equations; Parameters; Partial Differential Equations; Randomly occurring cyberattacks; State-saturated systems; Time delay; Uncertain occurring probabilities; Upper bounds; State-saturated systems; Time delay; Distributed extended Kalman filtering; Randomly occurring cyberattacks; Uncertain occurring probabilities
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02896-3

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.