Neural-Network-Based State Estimation for Nonlinear Stochastic Systems Under Token Bucket Communication Protocol

This article is concerned with the recursive neural network (NN)-based state estimation problem for a class of stochastic discrete time-varying systems subjected to both unknown nonlinear dynamics and the token bucket communication protocol. The token bucket protocol is utilized to determine whether the sensor signal is granted access to the network at each transmission instant, wherein the transmission may fail due to an insufficient number of tokens in the bucket. The objective of the addressed problem is to design a recursive NN-based state estimator such that, under the influence of the unknown nonlinear dynamics and the token bucket communication protocol, certain upper bounds of both the state estimation error covariance and the NN-weight (NNW) error covariance are guaranteed, while the explicit expressions of the NN-based estimator gain and the NN tuning parameters are derived. By employing two sets of matrix difference equations, two upper bounds for the state estimation error covariance and the NNW error covariance are established, and these upper bounds are subsequently minimized by parameterizing the NN-based estimator gain in terms of the solutions to the matrix difference equations. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed estimation approach.