Variance-Constrained Resilient \(H_{\infty }\) State Estimation for Time-Varying Neural Networks with Random Saturation Observation Under Uncertain Occurrence Probability

This paper studies the variance-constrained resilient \(H_{\infty }\) state estimation problem for discrete time-varying uncertain recurrent neural networks with random saturation observation under uncertain occurrence probability. In fact, the state estimation problem of stochastic recurrent neural networks with time-varying parameters has significant importance and wide applications. In order to characterize the realistic transmission process of neural signals, the phenomenon of random saturation observation is represented by introducing a random variable. In addition, the estimator gain is allowed to satisfy parameter perturbations to reflect the fragility of the estimator. The main objective is to present a finite-horizon resilient state estimation scheme without utilizing the augmentation method such that, in the presence of estimator parameter perturbations and random saturation observation, some sufficient criteria are obtained for the estimation error dynamical system satisfying both the pre-defined \(H_{\infty }\) performance constraint and the error variance boundedness. Finally, a numerical example demonstrates the feasibility of the presented resilient \(H_{\infty }\) SE method under variance constraint. From the engineering viewpoint, the proposed state estimation method under variance constraint has time-varying characteristics, which is suitable for online estimation applications. Moreover, both the state estimation and original neural state have the same order, which can reduce the computation burden.