State estimation for a class of artificial neural networks with stochastically corrupted measurements under Round-Robin protocol

Abstract

This paper is concerned with the state estimation problem for a class of artificial neural networks (ANNs) without the assumptions of monotonicity or differentiability of the activation functions. The measured outputs are corrupted by stochastic noise signal whose intensity is quantified by a nonlinear function. In order to accommodate the bandwidth limit of the communication channel between the ANN and the state estimator, an equal allocation scheme (i.e. Round-Robin protocol) of the communication resource is employed to effectively mitigate data congestions and save energies. A set of zero-order holders (ZOHs) is utilized to store the received measurements, such that the utilization of the received measurements can be maximized. An update matrix approach is developed to handle the time-varying yet periodic time-delays resulting from the adoption of the Round-Robin protocol. The aim of the proposed problem is to design a state estimator such that the error dynamics is exponentially ultimately bounded. A combination of the Lyapunov stability theory and the stochastic analysis technique is used to derive some easy-to-test conditions for the existence of the desired state estimator. The estimator gains are characterized by the solution to a convex optimization problem that is solved via the semi-definite programme method. Simulation results are given to demonstrate the effectiveness of the proposed estimation approach.

Keywords: Activation function; Artificial neural network; Noise intensity function; Nonlinearity; Round-Robin protocol; State estimation.