Research On Several Types Of Synchronization Control For Reaction-diffusion Neural Networks

Reaction-diffusion neural networks(RDNNs)not only have good features such as large storage,strong self-learning ability,and strong associative memory,but also can well simulate the reaction and diffusion phenomena of real systems.Nowadays,the synchronization of RDNNs has important applications in various engineering fields including secure communication,artificial locomotion,and population control.Thus,it is meaningful to study the synchronization of RDNNs.However,the existence of reaction-diffusion may result in instability to deteriorate system performance.Hence,in this thesis,four synchronization control problems: pinning sampled-data control,stochastic reliable control,stochastic sampling control,and time-space sampled-data control are studied for RDNNs.The main works are summarized as below.1.The pinning sampled-data control has been studied for synchronization of coupled RDNNs.First,combining pinning control and sampled-data control,by the theory of minimum spanning tree,a pinning sampled-data control mechanism is designed.The mechanism effectively reduce the amount of communications and save the control cost.Next,according to Lyapunov stability theorem,a sampled-instant-dependent Lyapunov-Krasovskii functional(LKF)is constructed,which can fully utilize the actual sampling information.Then,a inequality is newly proposed,which effectively relaxes the restrictions of the positive definiteness of the constructed LKF.And then,based on the LKF and the new inequality,sufficient conditions are derived to synchronize the coupled RDNNs.The desired pinning sampled-data control gain is precisely obtained.Finally,two numerical examples are presented to verify the effectiveness and merits of the theoretical results.2.The stochastic reliable control has been studied for synchronization of coupled RDNNs.First,considering the abrupt changes of the structure and parameters of systems,a coupled Markovian RDNN model with generalized transition rates is built.Next,a mode-dependent reliable control scheme with actuator failures is proposed.The control scheme has a good property of fault tolerance.Then,by constructing a LKF,a new synchronization criterion is established for coupled Markovian RDNNs.The constructed LKF can fully utilize the information on the slope of neuron activation functions.Finally,a numerical example is given to show the effectiveness of the proposed results.3.The stochastic sampling control has been studied for synchronization of RDNNs.First,a new switching system protocol is proposed for stochastic sampling control systems.The switching system protocol effectively improves the existing methods(the correlation between random variables is neglected).By the protocol,the stochastic switching sampled-data controller is designed,and the RDNN with stochastic sampling is transformed into a switching system.Next,by constructing a stochastic switching LKF,using inequality estimation techniques,Law of Large Numbers and Lagrange Mean Value Theorem,new synchronization in probability criteria are established for drive-response RDNNs.Then,when reaction-diffusion terms are not involved,the synchronization in probability problem is also studied for NNs with stochastic sampling.Finally,the feasibility and effectiveness of the proposed results are verified by two numerical examples.4.The time-space sampled-data control has been studied for synchronization of RDNNs.First,sampling in time domain and dividing the space domain,the time-space sampleddata control mechanism is designed.Next,by Poincaré-Wirtinger inequality,the generalized Poincaré-Wirtinger inequality is firtly proposed.By introducing more adjustable matrices,the generalized Poincaré-Wirtinger inequality can effectively reduce the conservatism of system performance criteria.Then,by constructing a sampled-instant-dependent LKF and using the generalized Poincaré-Wirtinger inequality,new exponential synchronization criteria in meansquare are derived for drive-response RDNNs.Meanwhile,according to the synchronization criteria,the time-space sampled-data controller is designed.Finally,a numerical example is given to verify the effectiveness of the theory results and show the superiority of the generalized Poincaré-Wirtinger inequality.