MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Online Solution of Linear Time-Varying Equations

Different from gradient-based neural networks (in short, gradient neural networks), a special kind of recurrent neural networks has recently been proposed by Zhang et al for time-varying matrix inversion and equations solving. As compared to gradient neural networks (GNN), Zhang neural networks (ZNN) are designed based on matrix-valued or vector-valued error functions, instead of scalar-valued error functions based on matrix norm. In addition, Zhang neural networks are depicted in implicit dynamics instead of explicit dynamics. In this paper, we simulate and compare Zhang neural network and gradient neural network for the online solution of linear time-varying equations. To do so, two important MATLAB-simulation techniques are employed. i) MATLAB routine “ode45” with a mass-matrix property is introduced. ii) Matrix derivatives are obtained by using MATLAB routine “diff” and symbolic math toolbox. Computersimulation results substantiate the theoretical analysis of Zhang neural network and gradient neural network for solving linear time-varying equations, especially when using a power-sigmoid activation function. In addition, such neural networks are simulated and compared in the presence of large implementation errors.