H_? Performance Analysis And Synchronization Control For Reaction-diffusion Neural Networks

Neural networks,as mathematical models to simulate behavior mechanisms of the brain for information processing,have been widely used due to theirs highly nonlinear characteristics and circuit achievability.However,when electrons move in some non-uniform electromagnetic areas,diffusion phenomena inevitably occur.Therefore,it is necessary to introduce the diffusion effect into the computational modeling of neural networks.In practice,reaction-diffusion systems have an important application background,which can be used to describe the state change process of neural networks,fluid systems and biological populations,etc.The H_?performance analysis of reaction-diffusion neural networks and the synchronization problem of coupled reaction-diffusion neural networks have attracted the attention of many researchers.From the perspective of practical engineering applications,some phenomena often occur in real systems such as time delays,random disturbances and component failures,etc.Therefore,it is of great practical significance to study the reaction-diffusion neural networks with time delays,random disturbance and subsystem interconnections etc.Based on the Lyapunov stability theory,the H_?performance analysis and synchronization control of reaction-diffusion neural networks are studied by using some techniques,such as Jensen's inequality,Wirtinger-type integral inequality and linear matrix inequality.The specific content is as follows:1.Consider a class of Markov jump reaction-diffusion neural networks with time-varying delays,and study their H_?performance analysis under Dirichlet and Neumann boundary conditions.Due to the existence of random cases,the structure and parameters of the system may suffer some unpredicted abrupt changes.Markov process,as an efficient method,can well describe this kind of jumping case.Because of the introduction of the diffusion terms,the structural equation form of the system is transformed from a general differential equation to a partial differential equation.In order to overcome some difficulties caused by the introduction of partial differential terms,a new integral term is introduced into the Lyapunov-Krasovskii functional,and the delay-dependent stability conditions of linear matrix inequalities are obtained by using some inequality methods,such that ensure the stochastic stability of the designed neural networks and satisfy prescribed H_?performance.Finally,the feasibility of the designed technique is certified by two examples.2.Consider a class of Markov jump reaction-diffusion neural networks via a disturbance observer-based method,and study its robust composite H_?synchronization control problem under Dirichlet boundary conditions.Due to the existence of disturbance effects,the performance of the aforesaid system would be degraded or even render instability of the system,therefore improving the control performance of closed-loop neural networks is the main goal of this paper.A composite disturbance rejection control strategy is adopted to improve the control performance of the closed-loop neural networks.The disturbance observer method is combined with the conventional state feedback control method to reject and attenuate the influence of disturbances.Then,based on Lyapunov stability theory,some criteria are established to ensure that the synchronization error system is stochastically stable and satisfies an expected H_?disturbance rejection-attenuation performance level.The controller gains are obtained by a conventional decoupling method,and the effectiveness of the proposed method is verified by a numerical example.3.Consider a class of coupled neural networks with reaction-diffusion terms via a fuzzy-model-based,and study its pinning synchronization control problem.Combining the results of the foregoing work,reaction-diffusion neural networks with coupled terms are considered.Different from the aforementioned neural networks,coupled neural networks,as a special case of complex networks,have more complex network nodes,which increases the difficulty of controlling network nodes.In order to overcome this thorny problem,an adaptive pinning control mechanism is adopted,that is,control a small number of nodes instead of all nodes to achieve the control purpose,which not only reduces the control cost to a certain extent,but also adjusts the coupling strength adaptively.At the same time,considering the nonlinear parameters existing in the system,the T-S fuzzy model can be used to model the system.Then,based on the appropriate Lyapunov function and combining the fuzzy set theory,some sufficient conditions to ensure that the resulting closed-loop system is stochastically stable and meets the preset H_?performance level are obtained.Finally,a numerical example is given to verify the accuracy and effectiveness of the proposed method.