Fixed-Time Synchronization Research For Several Types Of Networks

In recent years,networks have become useful modeling tools to describe the dynamic behavior of many natural and artificial systems.For example,community networks can describe social networks,and neural networks can simulate the perception and learning ability of human brain.The control of networks plays an important role in the research and application of networks,which has important theoretical significance and wide application value.In recent years,the fixed-time control of both integer-order networks and fractional-order networks has been widely concerned by scientists because it can obtain the estimated settling time without acquiring the initial conditions of networks in advance.Therefore,this thesis studies the fixed time synchronization of two kinds of networks.The thesis is divided into four chapters,the main contents are as follows:The first chapter summarizes the research significance and current research status of fixed-time synchronization control for integer-order complex networks and fractional-order neural networks,and clarifies the main research contents and main innovation points of this paper.In the second chapter,the fixed-time cluster synchronization problem of directed community networks is studied.A new Lyapunov function method is proposed,which leads to the settling time is not only independent of the initial value,but also independent of both the number and dimensions of nodes in the networks.This means the estimated settling time in this paper is more accurate and much tighter than the one in the existing results.By designing the corresponding state feedback controllers and using the fixed-time stability theorem,some new criteria are derived to ensure the community network to achieve cluster synchronization in fixed time.Finally,the correctness of theoretical analysis is verified by computer simulations.In the third chapter,we research the fixed-time synchronization of fractional-order inertial neural networks with time delays.Firstly,an appropriate method of two-parameter variable substitution is proposed to deal with the inertial terms.On this basis,by combining with Lyapunov stability theory,the corresponding sliding mode controllers and the sliding mode surface are designed,and some novel criteria are obtained for ensuring the fixed-time synchronization of fractional-order inertial neural networks.Compared with the existing results,the delayed terms are not involved in the controllers presented in this paper,and the obtained settling time is shorter.Finally,a numerical example is given to show the validity and feasibility of our theory results.In the last chapter,the research works of this dissertation are summarized.Furthermore,the possible improved methods are proposed and the prospects for the future works are made.