Recursive state estimation for delayed complex networks with random link failures and stochastic inner coupling under cyber attacks

This paper focuses on the filtering issue regarding a class of uncertain time-delayed complex networks (CNs) subject to random link failures (RLF) and stochastic inner coupling (SIC) under cyber attacks, where the attacks occur in a random way with uncertain occurrence probabilities. The phenomena of RLF and SIC are described via a Bernoulli distributed random variable and a Gaussian noise, respectively. The former reflects the presence or absence of connections between different nodes, while the latter presents the uncertainty of the inner coupling strength. In addition, denial of service attacks (DoSAs) and false data injection attacks (FDIAs) are both taken into account in the discussed cyber space, where the switching behavior of attack modes is described by two independent Bernoulli distributed random variables. A novel recursive estimator is constructed with consideration of RLF, uncertain time-delay, SIC and cyber attacks, wherein a state estimation error covariance upper bound (SEECUB) is obtained. And such upper bound is minimized via reasonable design of the estimator gain. Through theoretical deduction and analysis, it is proved that the presented SEECUB is uniformly bounded under certain conditions. Finally, the availability of the proposed filtering strategy and the gained results are verified through simulation examples.