1Zeroing Neural Networks for Control

1.1 Introduction

In addition to the remarkable features such as parallelism, distributed storage, and adaptive self‐learning capability, neural networks can be readily implemented by hardware, and have thus been applied widely in many fields [16]. The zeroing neural network (ZNN) as well as its variant (i.e. zeroing dynamic), as a systematic approach to the online solution of time‐varying problems with scalar situation included, has been applied to online matrix inversion [7], motion generation and control of redundant robot manipulators [3], and tracking control of nonlinear chaotic systems [8]. For example, a ZNN model with a nonlinear function activated is applied to the kinematic control of redundant robot manipulators via Jacobian matrix pseudoinversion in [9], which achieves high accuracy but cannot handle the bound constraints existing in the robots. In [10], present a finite‐time convergent ZNN model is presented for solving dynamic quadratic programs with application to robot tracking, which requires convex activation functions and cannot remedy the issue of joint‐limit avoidance. Such a ZNN method is further discretized to compute the solution to time‐varying nonlinear equations based on a new three‐step formula, which can be implemented on a digital computer directly. In addition, for the applications, ZNN is exploited in [3] to remedy the joint‐angle drift phenomenon of redundant robot manipulators by minimizing the difference ...

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