State estimation problem for fractional-order neural networks using event-triggered state observers

Abstract

This article considers the state estimation problem for fractional-order neural networks subject to external disturbances using event-triggered state observers. For the first time, a novel method based on a discrete-time event-triggered mechanism and a nonlinear fractional-order state observer is obtained. A new discrete-time event-triggered mechanism is first proposed. Then a new nonlinear fractional-order state observer based on the newly discrete-time event-triggered mechanism is designed to estimate state vectors of the fractional-order neural networks robustly. The discrete-time event-triggered mechanism is Zeno-free, and it helps reduce unnecessary continuous signal transmission. A fractional-order-dependent condition to guarantee the existence of the discrete-time event-triggered nonlinear fractional-order state observer is established. This condition is translated into a convex optimization problem, which can be solved easily by MATLAB. The solution to this problem minimizes the attenuation levels and thus reduces the error in estimating the state vector of the fractional-order neural networks. The effectiveness of the proposed method is illustrated by two numerical examples and simulation results.