On The Exponential Stabilization Of A Class Of Delayed Memristive Neural Networks

Artificial neural network,as a type of information disposal system,can imitate the structure and function of the human brain to process complex information.It has become a key method in the field of intelligent control and information processing.How to build an artificial neural net-work to accurately describe the dynamic behavior of the human brain neural network has attracted widespread attention in various fields.As a new type of non-linear element,memristor has the advantages of small size,low power consumption,variable resistance,nonvolatile and memory function.It has strong similarities in function with synapses in biological neural networks.There-fore,it is suitable to replace resistance to build artificial neural network.In recent years,the dy-namics of neural networks based on memristive modeling has gradually become a new hotspot in the field of neural network research.The stability of memristive neural networks(MNNs)and other related problems have become an important research topic in the modern control theory,which has extremely important practical significance.The main contents of this thesis include:(1)In the framework of the input delay method,the exponential stabilization of delayed MNNs is studied based on sampled-data control method.Firstly,the sampled-data controller is designed.Then,the LMI criterion for the stabilization of the delayed MNNs is obtained by con-structing a new time-dependent Lyapunov functional and combined with linear matrix inequality technology.The interval matrix method is used to deal with the memristive connection weights,and the information of the memristive connection weights is fully used,which reduces the con-servativeness of the obtained criteria.Finally,the effectiveness of the designed sampled-data con-troller and the established stabilization criteria are verified by numerical simulation.(2)The exponential stabilization of delayed MNNs is studied based on aperiodically inter-mittent control method.Firstly,an index called the largest proportion of the rest width(LPRW)in the control period is proposed to measure the allow sensor failure interval.Then,an aperiodically intermittent controller is designed.By constructing suitable Lyapunov functional in combination with interval matrix method and Halanay inequality,a stabilization criterion in algebraic form for delayed MNNs is established.Meanwhile,an algorithm is proposed to qualitatively analyze the relationship between the feedback gain and the LPRW.In contrast with the previous work,the interval matrix method is used to deal with time-varying connection weights,which can reduce the requirements for control gain and increase the interval of sensor failure while still maintaining the stability of the closed-loop memristive neural networks.Finally,the comparison of simulation results demonstrate that the obtained stabilization criterion has some advantages over the existing ones.