Synchronization Of Reaction-diffusion Neural Networks Based On Event-triggered Sampled-data Control

Reaction-diffusion neural networks（RDNNs）not only have good features such as strong self-learning ability,large storage,and strong associative memory,but also can well model the reaction and diffusion phenomena of actual systems.Synchronization is a natural phenomenon that exists widely in nature and reflects the overall coordinated behavior of individuals through information exchange.At present,the synchronization of RDNNs has been widely concerned by domestic and foreign scholars because of its important applications in secure communication,image processing and population control.However,due to the limited network bandwidth,problems such as packet losses,packet confusion and external disturbance may occur when data is transmitted in the channel,which will degrade system performance and even destroy the stability of the error system.Event-triggered sampled-data（ETSD）control can effectively reduce the impact of communication bandwidth limitation and improve resource utilization while meeting the system performance requirements,and is gradually replacing the traditional periodic sampled-data control strategy.Therefore,this paper studies the synchronization problem of RDNNs based on ETSD control.The main research contents and innovations are given as follows:1.For the output synchronization problem of space-varying RDNNs under random packet losses,an ETSD control method is proposed.Firstly,an ETSD control scheme based on spatially point measurements is designed.The implementation of this mechanism requires only few number of sensors and actuators,and can decrease unnecessary sampled-data to reduce the communication burden.Then,the stability of the synchronization error system is analyzed by Lyapunov direct method,and the sufficient conditions for the synchronization of space-varying RDNNs under random packet losses are obtained.Next,we acquire the desired ETSD control gain on the basis of linear matrix inequality（LMI）method.Finally,the effectiveness of the proposed method is demonstrated by one numerical example.2.For the extended dissipative output synchronization problem of delayed RDNNs under deception attacks,an adaptive ETSD control method based on spatially averaged measurements is proposed.Firstly,an adaptive ETSD control scheme is designed.The threshold in this scheme can be adjusted adaptively according to the current sampling and the latest transmitted signals,and the implementation of this scheme only needs few number of sensors and actuators.Secondly,under deception attacks,some sufficient conditions for stability and extended dissipative performance of the synchronization error system are established by utilizing Lyapunov-Krasovskii functional and inequality techniques.Then,by solving LMIs and selecting appropriate dissipative parameters,the adaptive ETSD control gains under passivity performance andL₂-L_∞performance are obtained respectively.Lastly,a numerical example is given to demonstrate the effectiveness of the proposed approach.3.For the synchronization problem of coupled RDNNs,a pinning ETSD control scheme based on spatially point measurements scheme is proposed.Firstly,combining pinning control and ETSD control,a pinning ETSD control strategy based on spatially point measurements is designed,which effectively reduces the network information transmission,saves the control cost and is easy to implement.Secondly,under the designed pinning ETSD controller,the stability of the synchronization error system is studied by Lyapunov direct method,and the sufficient conditions for the synchronization of the error system are obtained.Then,the gain of pinning ETSD controller is derived by LMI method.Finally,one numerical simulation example is given to illustrate the effectiveness of the proposed synchronization strategy.