Predefined-Time Noise Immunity ZNN Model for Dynamic Quaternion Least Squares Problem and Application to Synchronization of Hyperchaotic Systems
Lin Xiao, Penglin Cao, Yongjun He, Liu Luo, Linju Li
Abstract
Currently, there is a dearth of algorithms for solving the dynamic quaternion least squares problem (DQLSP), and the traditional numerical methods cannot solve dynamic problems effectively. To solve the DQLSP, a predefined-time noise immunity ZNN (PTNIZNN) model and a novel activation function are presented, building upon the traditional zeroing neural network (ZNN) model. The convergence time (CT) of the PTNIZNN model is only related to a predefined-time (PT) parameter, which makes it simpler to adjust the CT than the prior fixed-time convergence ZNN model. It is proved via mathematical deductive reasoning that the PT convergence and noise immunity of the PTNIZNN model hold when solving the DQLSP. In addition, a numerical example is given to demonstrate the correctness of mathematical deductive reasoning and the advantages of the PTNIZNN model. Finally, according to the design scheme of the PTNIZNN model, a new controller is designed to achieve the synchronization of the hyperchaotic Lorenz systems and applied to image encryption.