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. Zeroing neural network (ZNN) is one of the effective solutions to time-variant problems including time-variant linear equations. This paper 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 3D stereo reconstruction and motion control of a Franka Emika Panda robot, showing the efficacy of the proposed method.