An adaptive robust gradient-based recurrent neural network for solving time-varying linear matrix equation and its application

The time-varying (TV) problems frequently happen in various practical engineering fields. As for their solution, most neural network models are based on the classical gradient-based neural network (CGNN) with an evident lagging error, which is tailored for time-independent problems. Considering the wide range of applications of gradient-based algorithm in many fields, in this article, we propose an improvement to the CGNN model based on the Lyapunov control theory, resulting in an adaptive robust gradient-based recurrent neural network (ARG-RNN), which is demonstrated that it is an effective neural solver for the TV problems in theory and also substantiated by following the simulated real-valued and complex-valued linear matrix equations solving experiments and an angle of arrival (AoA) location application. Additionally, most neural network models are developed for noise-free environments, while noise is often unavoidable in practical applications. Therefore, the presented ARG-RNN is also verified to be capable of obtaining an exact solution even in the face of external constant noise, linear TV noise, or bounded random noise by the noise-tolerant experiments and comparisons.