Design and Analysis of a Novel Finite-Time Convergent and Noise-Tolerant Recurrent Neural Network for Time-Variant Matrix Inversion

Abstract

Matrix inversion ubiquitously arises in engineering. The so-called zeroing neural network (ZNN) is an effective recurrent neural network for solving time-variant matrix inversion. Without considering noises, the ZNN approach requires finite time or infinitely long time to converge to the exact solution. When perturbed by additive noises, the existing ZNN models exhibit limited ability to reject disturbances and are susceptible to be divergent. For instance, under time-variant bounded noises, steady-state residual errors of the existing ZNNs would be bounded. To make the steady-state residual errors arbitrarily small, infinitely long time is required and related design parameters must be set large enough or infinitely large, which is not realistic in practice. To overcome this situation, this paper for the first time systematically designs and analyses a finite-time convergent and noise-tolerant ZNN (FTNTZNN) that is capable of completely converging to the theoretical solution in finite time even under various types of noises. Theoretically, the finite-time convergence and disturbance-rejection properties of the FTNTZNN are rigorously proved. Comparative numerical results substantiate that the FTNTZNN model delivers superior convergence and robustness performance in solving time-variant matrix inversion and kinematic control of a robotic arm as compared with the existing ZNN models. The FTNTZNN model expands the current knowledge for designing neural-dynamic systems to solve matrix inversion, which can provide inspiration for other problems solving under noises.