Predefined-time robust adaptive gradient neural network for solving linear time-varying equations and its applications

Abstract

Adaptive gradient neural networks (AGNN) have been extensively employed as effective models for addressing time-varying problems. However, the existing AGNN are convergent in infinite time and only considered in noiseless environment. Consequently, the AGNN with a certain convergence time and noise tolerance is urgently required. Motivated by the advantages of predefined-time convergence, a novel predefined-time robust adaptive gradient neural network (PRAGNN) is developed for solving linear time-varying equations. It can be concluded that PRAGNN can efficiently obtain real-time solutions of linear time-varying equations within predefined time, independent of initial conditions, by properly selecting parameters. In the process of solving linear time-varying equations, PRAGNN can avoid matrix inversion, which reduces the computing cost compared with zeroing neural networks (ZNN). Furthermore, PRAGNN can completely resist both bounded vanishing noise and bounded non-vanishing noise. Numerical experiments demonstrate the effectiveness of PRAGNN. Finally, PRAGNN has been successfully utilized in 2-D dynamic positioning based on the angle of arrival (AOA) positioning algorithm, as well as in alternating currents (AC) computing.