Novel Insight into Time-Space Sampled-Data Mechanism for Quasi-Estimation of RDNNs

A state estimator based on a time-space sampled-data mechanism is proposed for reaction-diffusion neural networks with uncertain parameters over a rectangular domain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>. The specific sampling strategy is to establish a coordinate system for the two-dimensional space, divide the two coordinate axis into finite sampling intervals, and then take the midpoints of the respective sampling intervals as the coordinates of the sampling points. The objective is to further reduce the burden of communication by decreasing the number of spatial sampling points while maintaining satisfactory estimation performance. Sufficient conditions for the error system’s stability and the convergence region of quasi-estimation are derived by the Lyapunov function method and the improved Halanay’s inequality. Three numerical examples illustrate the validity and advantage of the proposed method.