A Strictly Predefined-Time Convergent and Noise-Tolerant Neural Model for Solving Linear Equations With Robotic Applications

Abstract

Nowadays, there are time-critical applications involving linear equations, such as the fault reconstruction problem, where hard response time constraints and robustness to external disturbances are expected. A zeroing neural network (ZNN) is one of the effective solutions to time-variant problems including time-variant linear equations. This article proposes a strictly predefined-time convergent and noise-tolerant ZNN (SPTC-NT-ZNN) to solve time-variant linear equations. Differing from the existing ZNN models, the designed SPTC-NT-ZNN is enhanced to be convergent in strictly predefined time while exhibiting noise tolerance. This guarantees the desirable timely convergence and robustness for time-critical applications. In theory, the strictly predefined-time convergence and noise-tolerance properties of the proposed SPTC-NT-ZNN are mathematically proved in a rigorous manner. Comparative validations are performed to verify that the SPTC-NT-ZNN outperforms existing typical ZNNs, regarding the convergence and robustness performance. To demonstrate potential applications, the SPTC-NT-ZNN is applied to 3-D stereo reconstruction and motion control of a Franka Emika Panda robot, showing the efficacy of the proposed method