Adaptive Finite-time Synchronization Of Delayed Neural Networks

As we all know,neural network is a mathematical model that can highly simulate the synaptic connection structure of human brain.And due to its wide application values in the field of signal processing,pattern recognition,parallel computing and optimization,it has caught great attention of experts and scholars at home and abroad.In artificial neural networks,time-delays often exist during the signal transmission procedure between neurons,which may be a source of oscillation and undermine the stability property of a system.Thus,it's of great importance to fully consider time-delays in neural networks.In addition,delayed neural networks can exhibit some complex dynamics,for instance: chaos.As a special chaotic phenomenon,chaos synchronization of neural networks has been widely studied in control science and engineering.And massive considerable achievements have been made to realize chaos synchronization of neural networks.In practical engineering fields,it is more desirable that synchronization can be realized as fast as possible,even within a limited time.Therefore,it is extremely appealing to introduce the concept of finite-time synchronization when dealing with the synchronization problem of delayed neural networks.In this paper,we investigate the issue of finite-time synchronization for delayed neural networks on the basis of the famous finite-time stability theory.The study of delayed neural networks is carried out by utilizing adaptive control approach,where the neural networks have identical structure and different structures,respectively.The specifics are summarized as follows:1.A delay-dependent adaptive controller for neural networks with time-varying delay and the same structure is designed.By utilizing Linear Matrix Inequalities method and finite-time stability theory and constructing appropriate Lyapunov-Krasovskii functional,sufficient conditions are derived such that synchronization of delayed neural networks can be achieve within a finite time.And the settling time for synchronization can be estimated by the derived formula.Finally,a numerical example is carried out to illustrate the effectiveness of the obtained theoretical results.2.The issue of finite-time synchronization for neural networks with mixed delays and the same structure is investigated.The mixed delays include time-varying delay and distributed delay.By taking advantage of adaptive control method,Jensen inequality,Linear Matrix Inequalities method and finite-time stability theory,sufficient conditions are attained to ensure the synchronization error dynamical system reach stabilization at zero equilibrium point within a finite time.And the settling time for synchronization can be estimated by the derived formula.Finally,a numerical simulation is presented to demonstrate the effectiveness of the obtained results.3.The study of finite-time synchronization for delayed neural networks that have non-identical structures and unknown system parameters is divided into two parts.First,we consider the time-varying is known in prior.A delay-dependent adaptive controller and its adaptive updated laws are proposed,and theoretical result is derived such that the drive-response system can arrive at synchronization in finite time.Second,we consider the time-varying delay is unknown and the states of the neural networks are norm bounded.And two delay-independent adaptive controllers are presented such that the drive-response system can be synchronized in finite time.Finally,two numerical examples are implemented to illustrate the correctness and effectiveness of the designed method.