The Synchronisation Problem of Chaotic Neural Networks Based on Saturation Impulsive Control and Intermittent Control

Zhengran Cao, Chuandong Li and Man-Fai Leung ()
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Zhengran Cao: Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronic and Information, Southwest University, Chongqing 400715, China
Chuandong Li: Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronic and Information, Southwest University, Chongqing 400715, China
Man-Fai Leung: School of Computing and Information Science, Faculty of Science and Engineering, Anglia Ruskin University, Cambridge CB1 1PT, UK

Mathematics, 2024, vol. 12, issue 1, 1-20

Abstract: This paper primarily focuses on the chaos synchronisation analysis of neural networks (NNs) under a hybrid controller. Firstly, we design a suitable hybrid controller with saturated impulse control, combined with time-dependent intermittent control. Both controls are low-energy consumption and discrete, aligning well with industrial development needs. Secondly, the saturation function in the chaotic neural network is addressed using the polyhedral representation method and the sector nonlinearity method, respectively. By integrating the Lyapunov stability theory, Jensen’s inequality, the mathematical induction method, and the inequality reduction technique, we establish suitable time-dependent Lyapunov generalised equations. This leads to the estimation of the domain of attraction and the derivation of local exponential stability conditions for the error system. The validity of the achieved theoretical criteria is eventually demonstrated through numerical experiment simulations.

Keywords: chaos synchronisation; neural networks; actuator saturation; hybrid controller; Lyapunov Stability Control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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