State estimation of complex networks with time-varying delays and model uncertainty based on graph neural network

In this paper, the state estimation problem is investigated for an array of complex networks with time-varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Graph neural network is employed to deal with the uncertainty and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. By using Lyapunov function, the parameters of the estimator and the updating laws of the weights of graph neural network can be obtained by the solutions to linear matrix inequalities and the estimation error to converge to zero can be guaranteed. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme.