Asynchronous Filtering For Markov Jump Repeated Scalar Nonlinear Systems

The repeated scalar nonlinearity is a typical nonlinear system description method,it usually represents a class of functions with nonlinear features,such as semi-linear function,sine function,saturation function,hyperbolic tangent function and activation functions widely used in neural networks,etc.The repeated scalar nonlinear system is a class of nonlinear systems described by discrete state equations with the repeated scalar nonlinearity.In practice,many problems can be modeled as the repeated scalar nonlinear system,such as recurrent artificial neural networks,hypercube neural network,digital control with saturated nonlinearity,etc.Since the parameters of the repeated scalar nonlinear system is time-invariant,it has certain limitations in simulating dynamic systems.Whereas,the repeated scalar nonlinear system with Markov jump parameters can break through the original limitations and make it better describe the characteristics of the actual dynamic system.In recent years,the asynchronous filtering problem of Markov jump repeated scalar nonlinear systems has received extensive attention from scholars.This paper mainly studies the asynchronous filtering problem of such systems from the following two aspects.1.For discrete-time Markov jump repeated scalar nonlinear systems,using the hidden Markov model and T-S fuzzy model,the asynchronous filtering problem of this system is studied.A partially modal dependent fuzzy asynchronous filter is designed to estimate the unmeasurable state variables in the system.The uncertainty and random nonlinearity of the system are considered,based on the T-S fuzzy theory,using the method of quantitative control,a mode-dependent diagonally dominant Lyapunov function is constructed,and sufficient conditions are given to ensure that the filtering error system is stochastically stable and satisfiesH_∞performance.Finally,two simulation examples are used to verify the correctness of the conclusion and the effectiveness of the method.2.For discrete-time Markov jump repeated scalar nonlinear systems,the asynchronous filtering problem of this system with deception attacks is studied.To alleviate the communication burden in a shared network,an event-based try-once-discard protocol is forwarded to regulate whether to release the measurements and which ones to release.A hidden Markov model with partially unknown transition probability is introduced to describe the modal asynchrony between the system and the filter.On this basis,a mode-dependent asynchronous filter is designed to estimate the unmeasurable state variables in the system.A mode-dependent diagonally dominant Lyapunov function is constructed,and sufficient conditions are given to ensure that the augmented filtering error system is stochastically stable and satisfiesH_∞performance.Finally,the correctness of the conclusion and the effectiveness of the method are verified by a numerical example.