Research On Dynamic Analysis And Control Of Neural Networks With Delays Via Event-based Control

The analysis and control of the dynamical behaviors have become hot research topics for delayed neural networks including memristive neural networks,switched neural networks in recent years,as the delayed neural networks have been applied in various fields such as combinatorial optimization,image encryption,pattern recognition,secure communication,associative memory and other fields,which has attracted a lot of attention of researchers from different fields.Meanwhile,the analysis and control of the dynamics of delayed neural networks are the premise of neural dynamics optimization and associative memory model design as well as the scientific and engineering applications of neural dynamics models.Therefore,it is of theoretical significance to research the analysis and control of the dynamics of delayed neural networks.In addition,with continuous development of neural networks,the scale of delayed neural network control systems is expanding,and the amount of data transmitted is also increasing.However,in the practical application of delayed neural network system,the communication cost,the network bandwidth,and the resource of network nodes are usually limited.In order to ensure that the cooperative tasks can be successfully achieved,it is necessary to design more reasonable control protocols for delayed neural network systems.Compared with the classic time-driven control strategy,event-triggered control strategy has significant advantages in saving system resources,reducing communication frequency,and relieving the pressure of data transmission of delayed neural networks.Therefore,in order to save system resources and improve control performance,it is of great economic benefit and practical significance to design an appropriate event-triggered control strategy to investigate the dynamics of delayed neural networks.In this dissertation,the dynamical analysis and control of several kinds of delayed neural networks are investigated mainly based on Lyapunov stability theory,matrix measure method and event-triggered control theory.This dissertation is divided into five chapters and organized as follows:In the first chapter,we introduce the related backgrounds and significance of neural networks,the development tendency on the analysis and control of the dynamics of delayed neural networks.Furthermore,the significance and developments of the analysis and control are presented for the dynamics of delayed neural networks based on event-triggered control.The main contents and arrangements of this dissertation are also explained according to the above discussions.In the second chapter,the passification problem are investigated for delayed memristive neural networks via event-triggered control.Firstly,by designing a static event trigger strategy and a dynamic event trigger strategy,the passification problems are investigated for memristive neural networks with time-varying delays under these two kinds of event-triggered control respectively.Then,several sufficient conditions of the passification are obtained for delayed memristive neural networks based on event-triggered control.Meanwhile,the passification algorithm is presented for the proposed system via event-triggered control.In addition,to avoid Zeno behaviour,the existence of positive lower bounds is approved for the inter event time.In the third chapter,the stabilization issue is analyzed for memristive neural networks with mixed time-varying delays via continuous/periodic event-based control.Firstly,the time-varying discrete and distributed delays are taken into account in the memristive neural networks.Then,by designing a continuous sampling event trigger control scheme and a dynamic periodic sampling event trigger control scheme,several sufficient conditions are provided for asymptotic stability of the delayed memristive neural networks system.Besides,there exist some positive lower bounds of the inter event time of the two event trigger control schemes,which shows the Zeno behaviour will not happen.Under these two control schemes,the control costs can be effectively saved through reducing the number of controller updates during the operation of the physical system.And the derived display expression of the sampling period could be references for engineers to adjust the sacrificing degree of the system performance and the saving degree of control cost in actual needs.In the fourth chapter,the synchronization problems are discussed for memristive neural networks with leakage delay and parameters mismatch via eventtriggered control.A kind of delayed memristive neural network model is proposed with leakage delay and parameters mismatch,and the leakage delay is also timevarying,which makes the proposed models more realistic and practical than earlier results.Next,the complete synchronization is analyzed the proposed system with state-dependent parameters mismatch via static or dynamic event-triggered control,then the quasi-synchronization is analyzed for the proposed system with function-dependent parameters mismatch by event-triggered control.Meanwhile,instead of deriving complex linear matrix inequalities,the p-norm and matrix measure method are adopted to greatly reduce the computational complexity and the conservativeness of the obtained results.Besides,the generalized Halanay inequality are adopted to analyze the quasi-synchronization,and the state errors are able to reach arbitrarily small if the control gains are appropriate.Finally,the Zeno behaviour can be excluded by theoretical analysis.In the fifth chapter,the exponential synchronization issues are explored for switched neural networks with mixed time-varying delays via static/dynamic eventtriggering rules.A kind of switched neural network model is proposed with timevarying delays and distributed delays.Then by designing static event-triggering rule and adaptive dynamic event-triggering rules,some sufficient conditions of exponential synchronization of the proposed system are obtained.Besides,by proving that the time interval between two successive trigger events has a positive lower bound,the Zeno behaviour will not appear.Finally,two illustrative examples are provided to demonstrate the validity and superiority of the obtained results.