On Stabilization And Synchronization Control Of Delayed Memristive Neural Networks

Recently,with the rapid development of memristor theory and its wide applications in various fields,the dynamical analysis of the memristor-based neural network models has become a new topic in the field of neural network.Memristor is a nonlinear memory resistor.The values of resistance depend on the electric charge passing through it.When the voltage is turned off,the memristor remembers its most recent value.At present,the regarding neurophysiology has shown that memristors have the ability to simulate the synapses of brain neurons.It is more suitable to establish artificial neural networks instead of resistors.Apparently,the introduction of memristor greatly enriches the dynamics of neural networks,which brings new opportunities and challenges to the theoretical and applied research of neural networks.Therefore,it is of great significance to investigate the dynamics and control of memristive neural networks.In this dissertation,according to the properties of capacitance,memristive neural networks are divided into integer-order memristive neural networks(IMNNs)and fractional-order memristive neural networks(FMNNs),and their dynamical behaviors are investigated,respectively.It should be mentioned that memristive neural networks are essentially state-dependent switched system with discontinuous right-hand sides.In this case,the classical definition for the solutions of ordinary differential equations is not applicable.The solutions of MNNs should be considered in Filippov's sense.Accordingly,the theories of differential inclusion and set-valued mapping are usually applied to study the stabilization and synchronization of memristive neural networks in the sense of Filippov solution.The contributions of this dissertation are summarized as follows:(1)The global stabilization of delayed IMNNs is addressed via switching event triggered control.First,by analyzing the merits and drawbacks of traditional event triggering schemes,a switching event triggering mechanism on the basis of exponential attenuation is presented.The novel event triggering mechanism can reduce the data transmission frequency while satisfying the requirement of system performance.Then,by utilizing time-dependent and piecewise Lyapunov functionals,and matrix norm inequalities,a joint design scheme is presented for the feedback gain and trigger parameters.It has been shown that the closed-loop system can achieve global asymptotical stability.Finally,some comparison simulation results demonstrate that the novel event triggering scheme has some advantages over the existing ones.(2)The quasi-synchronization of delayed IMNNs is discussed via aperiodically intermittent control.Considering the interruption or missing measurement of feedback signal in the case of sensor failure,an aperiodic intermittent controller is designed to guarantee control precision.First,the concept of asynchronously switching time interval is proposed to describe the phenomenon when the drive-response IMNNs switch their connection weights asynchronously.Then,two new upper bound for the p-norm of interval matrix and two differential inequalities are established,respectively.Combined with the matrix measure method,the quasi-synchronization criterion and the expression of prediction error are obtained.The stability analysis displays that the error system eventually converges to a bounded region.Finally,simulation results show the effectiveness of the designed controller and quasi-synchronization criterion.(3)A 3D-FMNN model with discontinuous memductance functions is established and the corresponding nonlinear dynamics is analyzed.The effects of fractional-order and switching jump on the dynamical behavior of the system are qualitatively analyzed.The dynamic bifurcation behavior of the system depending on fractional order,memductance and switching threshold is clarified.Different from the period-doubling route to chaos,this dissertation reveals that the mechanism behind the emergence of chaos for the 3D-FMNN is the intermittency route to chaos.(4)The quasi-synchronization of delayed FMNNs under continuous-time control is discussed.First,a new lemma on the estimate of Mittag-Leffler function is derived,which plays a key role in the estimate of synchronization error bound and extends the application of Mittag-Leffler function.Then,by choosing an appropriate fractional-order Lyapunov functional in combination with the maximum method and interval matrix method,the relationship between the upper bound of the synchronization error and the feedback gain is presented.Numerical analysis shows that the quasi-synchronization criterion is superior to some existing works.(5)The complete synchronization of delayed FMNNs via quantized control is investigated.First,considering that LMI stability criteria,for delayed fractional-order nonlinear systems,can not be established based on the existing works,a new fractional Lyapunov functional is established.Then,a quantized state feedback controller and a quantized coupling state feedback controller are designed,respectively.In combination with the novel fractional-order Lyapunov functional,a joint design scheme of the quantized parameter and feedback control gain is established,which can guarantee the global asymptotic stability of error system.Simulation results demonstrate the validity of the designed quantized controller and synchronization criteria.