Co-Design of Finite-Time Convergence and Noise Suppression: A Unified Neural Model for Time Varying Linear Equations With Robotic Applications

Abstract

Computing time-varying linear systems is widely encountered in engineering practice and scientific computation. Dynamic neural networks, as a class of modeling approaches, have been intensively explored in recent decades for solving linear equations. The time-varying nature of this problem and the noisy workspace for many engineering practice require two features of practical design: 1) fast convergence in time and 2) robustness against noises and disturbance. Existing solutions usually decouple the problem into two steps by designing a fast-convergent neural controller and then topped with an additional low-pass filter to reach noise robustness. However, due to the interplay of the mentioned two dynamical parts, the overall system may lose stability if the parameters are not well tuned. In this paper, we establish the first dynamical neural model for simultaneously achieving fast-convergence, particularly finite-time convergence, and noise-robustness, with the capability to reject the unknown noise when it is constant or varies slowly. To do so, a superior design formula activated by noise-tolerant nonlinear functions is proposed to enhance the capability of zeroing neural networks (ZNNs), achieving denoising and finite-time convergence in a unified design. According to this design formula, a novel recurrent neural network (RNN) with finite-time convergence and inherently noise-suppression performance [thus termed the finite-time robust RNN (FTRRNN)] is developed and applied to robotic motion tracking illustrated via time-varying linear equation system solving. Furthermore, theoretical analyses on the global stability, the finite-time convergence and the denoising ability of the proposed design formula and the corresponding FTRRNN model are presented in details. The upper bound on the convergence time is also analytically derived. A numerical example is supplied to verify the superior property of the FTRRNN model to the ZNN model according to the results of computing time-varying linear equation system in the presence of additive noises. Finally, an application to robotic motion tracking is presented to show that the presented FTRRNN model can successfully realize the ellipse-path tracking control of a planar two-link manipulator in front of the external disturbances, while the conventional ZNN model fails under the same conditions.