An Adaptive Gradient Neural Network to Solve Dynamic Linear Matrix Equations

Abstract

In this article, the existing approaches, including numerical algorithms as well as neural networks to solve dynamic linear matrix equations, have been presented and reviewed. Specifically, the conventional gradient recurrent neural networks (CGRNNs) and the conventional zeroing neural networks (CZNNs) are successively provided to solve the dynamic problems and linear matrix equations, both of which manifest inherent limitations during the solving procedures. To remedy the drawbacks on convergence time, nonzero residual error, and large computational load of the traditional models, an adaptive gradient recurrent neural network (AGRNN) to solve dynamic linear matrix equations is proposed. This proposed inversion-free model possesses rapid convergence rate and accurate calculated solutions. Moreover, theoretical analyses guarantee the advantages of the AGRNN compared with the CGRNN and the CZNN to solve dynamic linear matrix equations. Finally, three numerical experiments, and applications to a PUMA 560 robot motion planning and a mobile subject localization based on angle-of-arrival technique are implemented to testify the advantages of the AGRNN.