Zeroing Neural Networks for Control

• Published in: Kinematic Control of Redundant Robot Arms Using Neural Networks pp. 1 - 16
• Main Authors: Li, Shuai, Jin, Long, Mirza, Mohammed Aquil
• Format: Book Chapter
• Language: English
• Published: Chichester, UK Wiley 2019; John Wiley & Sons, Ltd
• Edition: 1
• Series: Wiley - IEEE
• Subjects: activation functions; bound constraints; inequality constraints; real‐time dynamic quadratic programming; time‐varying optimization problem; zeroing neural network models; Jacobian matrices; Manipulators; Dynamic programming; Mathematical model; Neural networks; Optimization
• ISBN: 9781119556961; 1119556961
• DOI: 10.1002/9781119557005.ch1

This chapter presents zeroing neural network (ZNN) models that are able to deal with nonconvex projection set in the activation functions, while the existing solutions require the projection set to be convex. It solves a time‐varying optimization problem with inequality and bound constraints, which opens a door to the research on solving time‐varying constrained optimization problems in an error‐free manner. There are two limitations in the existing research on ZNN, i.e. lacking the technique for handling inequality and bound constraints when solving dynamic optimization problems and requiring the activation function to be odd and monotonically increasing. The chapter overcomes these limitations by proposing ZNN models, allowing nonconvex sets for projection operations in activation functions and incorporating new techniques for handling inequality constraint. Finally, illustrative simulation examples are provided and analyzed to substantiate the efficacy and superiority of the presented ZNN models for real‐time dynamic quadratic programming subject to equality and inequality constraints.