Exponential Synchronization Of Delayed Neural Networks With Stochastic Switching And Quantized Control

In recent years,the synchronization and control of chaotic systems have aroused great interest of many scholars,and a series of important research results have emerged.Since neural networks can exhibit chaotic behavior as long as their parameters and delays are properly chosen,they have also been widely concerned.Stochastic switching phenomena such as the change of external environment,failure or repair of system components are common in real life,which usually results in the change of system structure or parameters and make them chaotic.Obviously,the dynamics of such systems is more complex than that of systems with constant parameters.Considering the advantages of quantization such as saving channel resources and preventing channel congestion,this paper comprehensively studies the exponential synchronization problem of two kinds of neural networks under the influence of delay and stochastic switching by quantized control strategy.The specific research contents are stated as follows:Chapter 2 considers the problem of exponential synchronization of semi-Markovian coupled neural networks with bounded time-varying delay and infinite-time distributed delay(mixed delays)is investigated.Since semi-Markov switching occurs by time-varying probability,it is difficult to capture its precise switching signal.To overcome this difficulty,a tracker is used to track the switching information with some accuracy.Then a quantized output controller is designed by using the tracked information.Novel LyapunovKrasovskii functionals with negative terms and delay-partitioning approach,which reduce the conservativeness of the obtained results,are utilized to obtain linear matrix inequalities(LMIs)conditions ensuring the exponential synchronization.Moreover,an algorithm is proposed to design the control gains.Our results include both those derived by modedependent and mode-independent control schemes as special cases.Finally,a numerical simulation validates the effectiveness of the theoretical results.Chapter 3 considers global exponential synchronization almost surely for a class of switched discrete-time delayed neural networks.Different from the traditional average dwell time switching(ADT),a novel mode-dependent average dwell time(MDADT)based transition probability(TP)is established.Since different modes have different probabilities of being activated,it is more practical to combine TP with switching law.Considering the external disturbance,the feasibility of designing controller and control cost,a dynamic quantized output controller based on the actuator fault is designed.And exponential synchronization condition is obtained by using Lyapunov theory and new analysis techniques.Furthermore,our results get rid of the limitation of most of the existing results on the dwell time of the subsystem.i.e.the upper bound of the dwell time of the asynchronization subsystem cannot exceed a threshold,and the lower bound of the dwell time of the synchronization system cannot be less than a fixed constant.Finally,a numerical simulation verifies the effectiveness of the theoretical analysis.