A resilience approach to state estimation for discrete neural networks subject to multiple missing measurements and mixed time-delays

In this paper, the resilient state estimation problem is investigated for a class of discrete recurrent neural networks (RNNs) subject to mixed time-delays, missing measurements and stochastic disturbance. The mixed time-delays consist of randomly occurring time-delay and distributed sensor delays, where a random variable obeying the Bernoulli distribution is employed to characterize the phenomenon of randomly occurring time-delay. In addition, the phenomena of the multiple missing measurements are characterized by introducing a set of mutually independent random variables, which reflect that each sensor could have individual missing probability. Meanwhile, the additive variation of the estimator gain is considered to reflect the possible parameter deviations when implementing the state estimation algorithm. Our main purpose is to design a resilient state estimator such that, in the presence of multiple missing measurements, randomly occurring time-delay and distributed sensor delays, the estimation error dynamics is exponentially stable in the mean square. A sufficient condition is established to guarantee the existence of the resilient state estimator and the explicit expression of the desired estimator gain is given based on the solutions to some matrix inequalities. Finally, we use a numerical example to verify the validity of the presented resilient state estimation method.