Gradient Neural Dynamics Based on Modified Error Function

Abstract

The present study is devoted to methods for the numerical solution to the system of equations AXB=D. In the case certain conditions are met, the classical gradient neural network (GNN) dynamics obtains fast convergence. However, if those conditions are not satisfied, solution to the equation does not exist and therefore the error function E(t):=AV(t)B-D cannot be equal to zero, which increases the CPU time required for the calculation. In this paper, the solution to the matrix equation AXB = D is studied using the novel Gradient Neural Network (GGNN) model, termed as GGNN(A,B,D). The GGNN model is developed using a gradient of the error matrix used in the development of the GNN model. The proposed method uses a novel objective function that is guaranteed to converge to zero, thus reducing the execution time of the Simulink implementation. The GGNN-based dynamical systems for computing generalized inverses are also discussed. The conducted computational experiments have shown the applicability and advantage of the developed method.