Researches On Exponential Stabilization And Synchronization Control Of Inertial Neurodynamic System With Mixed Delays

The neurodynamic system has a great development in the area of interdisciplinary like mathematical sciences,control sciences as well as information sciences,which is a nonlinear system that can imitate the structure and functions of the human brain.It is worth noting that,the neurodynamic system with inertial terms can supply more sophisticated bifuracton behavior and chaos.More often than not,a class of inertial neurodynamic system are widely used in imfromation processing and image encrytion due to its broad background in biology.Compared with first-order derivative neural system model,the neurodynamic system with inertial terms described by second-order differential equation which has more complex daynamic behavior.Consquently,it is significant and essential to investigate the model of inertial neurodynamic system in the field of theory and application.In this paper,we deeply research the problem of global exponential stabilization,global synchronization control,fixed-time stabilization,predfined-time anti-synchronization control as well as fixed-time/predefined-time projective synchronization of inertial neurodynamic system model.Moreover,the obtained results of synchronizaiton are appiled into the Image Encrytion.We aim to estabilish a series of theoretical body of konwledge to deal with the problem of asymptotic time and fixed-time synchronization control for continuous and discontinuous of inertial neurodynamic system model,which develop and extend the previous related works.The main works of this paper are summarized as follows:Exponential stabilization for a class of fuzzy inertial neural networks(FINNs)with mixed delays is considered.Based on the case of 2-norm,by making useful Lyapunov functions and feedback controllers,several new criteria are achieved to get global exponential stability of the discussed FINNs.It is worth noting that,in this paper,the non-reduced-order method are considered to study such problem of global exponential stabilization,and the algebraic criteria for global exponential stabilization are related only to the system parameters and controller gain,which has less conservation than the reduced-order method.Synchronization control for a class of FINNs with mixed time delayed is investigated.As to corresponding drive-response system of delayed FINNs,anlyzing the effection of the initial state and parameter changes on the dynamic characteristics of the system from the attractor phase diagram.Based on Lyapunov stability theory,the FINNs can reach synchronization control by constructing non-reduced order method and adaptive control strateies.The problem of fixed-time stabilizaiton(FTS)and fixed-time projective synchronization(FTPS)for the chaotic inertia neural networks(INNs)with mixed delays is solved.In this article,by making use of direct approach and designing simple and practical Lyapunov functions,the sufficient conditions for the FTS and FTPS of the considered INNs are established under the state feedback control strategy.The comparative studies show that the theory results obtained by using the non-degenerate method in this paper further enrich and improve the existing results of related reduced order method and non-reduced order method.Anti-synchronziation in predefined-time for FINNs with mixed time delays is researched.In the light of predefined-time stability theorems,by employing two distinvtive bilayer predefined-time control inputs,the investigated FINNs can get antisynchronization which the setting time can not influenced by initial values and other parameters of system.Sufficient conditions are converted to a type of algebraic inequalities,some numercial examples and applications are illustrated to verify the effective of proposed theory results.Fixed-time projective synchronization(FTPS)and Predefined-time projective synchronization(PTPS)for a class of discontinuous fuzzy inertial neural networks(DFINNs)with mixed time delays is investigated.Using differential inclusion theory,Lyapunov stability theory,measurable choice theory and inequality deflation techniques,two types of effective fixed-time and predefined-time feedback controllers are constructed to achieve PTPS in a unified framework which based on different FTPS of this system.And new results are also given for the fixed/predefined time projective synchronization of DFINNs,the theoretical resulting finally are applied to image encryption and decryption.