Research On Convergence Time And Energy Consumption For Nonlinear Neural Networks

With the development of artificial intelligence,neural networks,as an indispensable part of artificial intelligence research,have caused a wave of research in scholars in different fields.Stability,as a prerequisite for the successful application of neural networks in practice,has always been an enduring subject in theoretical research.In practical applications,the issue of efficiency is often the first factor to be considered,which requires 'quick and save' to complete the set tasks.The finite-time stability(stabilization)of the studied system and the energy consumption estimation have naturally become important research contents.Aiming at the problem of finite-time stability(stabilization)and energy consumption estimation,the main research contents of this paper are as follows:Firstly,Chapter 2 studies the finite-time stabilization and energy consumption of a class of delay-free nonlinear neural networks.A closed-loop control method is used to construct a global switching controller.By constructing a suitable Lyapunov function,sufficient conditions for the finite time stabilization of the system are given,and the upper bound of the control time and energy consumption required to realize control is estimated.Secondly,considering the influence of delay in practical applications,Chapter 3studies the problem of finite-time stabilization and energy consumption for a class of delayed nonlinear neural networks.By improving the controller in Chapter 2 and using the comparison theorem of functional differential equations,sufficient conditions for finite-time stabilization of delayed nonlinear neural networks are obtained,and upper bounds for control time and energy consumption are given.The result of this chapter is a further generalization of Chapter 2.Again,in Chapter 4,by constructing a contraction mapping,using differential inclusion and set-valued mapping theory,a judgment of a fractional-order memristive neural network with a unique and finite-time stable equilibrium point at order 0 < ? <1 is given.At the order of 1 < ? < 2,a new criterion for the finite-time stability of the system solution is given by using the Laplace transform and the inverse transform.Finally,for different research contents in Chapter 2-4,we give numerical examples to prove the validity of the results.This research topic enriches the related results in neural network stability and controllability analysis.Meanwhile,it provides theoretical support for the application of neural network in intelligent control and artificial intelligence.