Research On Synchronous Control Of Three Kinds Of Complex Dynamical Networks

With the development of complex dynamic network(CDN)systems research,the synchro-nization research of CDN systems have far-reaching theoretical significance and strong prac-tical significance.The synchronization goal has changed from asymptotic synchronization to exponential synchronization,from finite time synchronization to fixed time synchroniza-tion,and the research methods are becoming more and more mature.However,there are still some areas to be improved in the synchronization research of CDN systems.Under the framework of control theory,this thesis considers the function projective synchronization(FPS)of neutral CDN systems,fixed-time stochastic synchronization(FTSS)of memristor-based neural network(MNN)systems with mixed time delay and fixed time matrix projec-tive synchronization of MNN systems with different node dimensions.The main researches of this thesis are listed as follows:1.We focus on the problem of FPS of neutral CDN systems with unknown time-varying coupling strength.Firstly,the separation principle is used to deal with the continuous non-linear function.Secondly,based on linear system theory and adaptive control method,adap-tive controller with adaptive update law is designed to make the controlled systems achieve adaptive FPS.By proving the boundedness of the Lyapunov-Krasvoskii functional on[0,T),the asymptotic convergence of the error system,and the boundedness of all signals in the closed-loop system in the sense of L_T~2norm,respectively,it can be concluded that the neutral CDN systems realizes the adaptive FPS.2.We are devoted to studying the FTSS of MNN with mixed delays.Under the Filippov framework,by using the theory of differential inclusion and extremal mapping,a linear feed-back controller is designed to make the system achieve FTSS synchronization,which implies synchronization settling time is independent of the initial state.By taking different values in the convex hull,the discontinuous systems are transformed into continuous systems.Thus,all solutions are defined in the meaning of Filippov sense in this case.It is worth noting that not only the influence of time-varying time delay and distributed time delay is considered,but also the role of stochastic factors is considered.In the end,by using comparison prin-ciple,it is finally proved that FTSS synchronization is realized under the designed controller.3.We mainly consider the fixed-time matrix projective synchronization of MNN with d-ifferent node dimensions.The feedback controller is designed by introducing a matrix of appropriate dimensions into the error systems to ensure that the systems achieve fixed-time matrix projective synchronization.In addition,the sufficient conditions for the projective synchronization of the fixed time lag matrix are given.Firstly,under the extremal mapping and the differential inclusion theory,the discontinuous systems are transformed into contin-uous systems.Secondly,a matrix of appropriate dimension is defined in the error systems and the feedback controller is designed.Finally,combined with the fixed-time stability the-orem,an appropriate Lyapunov-Krasvoskii functional is constructed to make the systems achieve fixed-time matrix projective synchronization.Finally,the research content of the full text is summarized and prospected,respectively.Summarize the main content of the research in each chapter,point out the advantages and disadvantages of the research problems,put forward the areas that need to be strengthened and improved.In the future research work,we will devote ourselves to further research on these aforementioned problems.