Finite-time Control And Applications Of Neurodynamic System With Inertial Terms

The neurodynamic system with inertial terms is not only an ideal tool for the nervous system to generate chaos and bifurcation,but also has a strong biological background.The study of this type of neurodynamic system can better reflect the characteristics of biological neural networks.In this paper,the finite-time stabilization and synchronization control of such neural dynamic system with inertial terms are studied in the real number domain and the complex number domain,and some important conclusions have been presented.In addition,these results are also applied to the Pseudo-random Number Generator and Image Encryption.The specific research content is as follows:The finite-time stabilization of a class of delayed inertial neural networks with state-dependent switching is studied.Through variable substitution,the second-order inertial neural networks are equivalently converted into the first-order differential equations form,and then with the help of differential inclusion theory,non-smooth analysis,finite-time stability theory and inequality skills,some new algebraic criteria are given to ensure the finite-time stabilization of the delayed inertial neural networks.These algebraic criteria here are given in the form of p-norm,and the time-varying delays of the neural system are not required to be differentiable.Furthermore,the obtained results here extend some of the existing outcomes and are less conservative.In the case of switching inertial neural networks with infinite mixed delays and different activation functions,under the designing a new hybrid switching adaptive controller and the corresponding adaptive update law,the sufficient conditions are obtained for the achievement of finite-time lag synchronization of inertial neural drive-response system by using a non-reduced method.The unbounded delays here includes bounded delays and proportional delays as special cases,and compared with the reduced-order method,the non-reduced method is more concise and practical.So,the results here improve and supplement the existing related results.The finite-time stabilization of complex-valued inertial neural networks with infinite time-varying delay is analyzed,where the complex-valued inertial neural networks are not decomposed into equivalent real-valued subsystems.With the help of Lyapunov's stability theory,the properties of complex numbers and analytical skills,algebraic criteria that can ensure the stabilization of complex-valued inertial neural networks in a finite-time are derived.Compared with separating the real and imaginary parts of complex-valued parameters,the processing method here is very natural,and the conclusion form is also quite simple.The p-norm fixed-time synchronization of delayed complex-valued inertial neural works is discussed.By decomposing the complex-valued inertial neural network into first-order real-valued subsystems,and combining analysis technology and Lyapunov stability theory,the algebraic criteria containing more parameters for fixed-time synchronization of such complex-valued inertial neural networks are established.Compared with the previous synchronization results based on 1-norm or2-norm,these algebraic criteria including p-norm and more parameters can show its own superiority and flexibility.