Synchronous Control Of Inertial Neural Networks With Time Delay

This paper mainly studies the fixed-time synchronization of inertial neural networks,using rigorous mathematical techniques such as definite integral and inequality techniques,and deriving a new criterion related to the stability of fixed-time.Then the new criterion is further improved after introducing a new lemma.Therefore,based on the new criterion and the improved criterion,the fixed time synchronization of the memristive fuzzy inertial neural network is studied by using a time-delay-related feedback controller.In addition,using the relevant new properties of the obtained complex-valued sign function,we directly study the finite-time and fixed-time anti-synchronization control of the discontinuous complex-valued inertial neural network.Finally,the numerical simulations performed verify the accuracy of our theoretical results.This paper is composed of four chapters.The first chapter is the introduction.First,it briefly summarizes the research status of the dynamic behavior of inertial neural networks.Secondly,the current research status of memristive neural networks and complex neural networks are introduced.Thirdly,the development status of the synchronization problem of neural network is explained.Finally,some basic mathematical definitions are given throughout the paper.In the second chapter,based on the strict mathematical techniques such as definite integral and inequality techniques,a new criterion for fixed-time stability is obtained,and the criterion is further improved.Secondly,via comparison,it is concluded that the upper bound of stability time obtained by the new criterion is smaller than that by the existing fixed time stability criterion.Finally,the fixed-time synchronization of memristor-based fuzzy inertial neural networks with proportional delays is studied by using the new criterion,and several sufficient conditions are given.The third chapter mainly investigate discontinuous complex-valued inertial neural networks with leakage and time-varying delays about finite-time and fixed-time synchronization.At first,a leakage delay and discontinuous activation functions are introduced into the complex-valued inertial neural networks.Then by utilizing complex-valued sign function and introducing several new properties,so that the complex-valued neural networks can be studied without separation.Based on the nonseparation method,novel controllers are constructed to realize finite-time and fixed-time synchronization of discontinuous complex-valued inertial neural networks.The fourth chapter mainly makes a comprehensive summary of the work of the full text,and gives the contents that need to be further studied in order to continue the research later.