Synchronization In Two Classes Of Nonlinear Dynamical Systems

The main research content of the article includes two parts.In the first part,a discrete fractional-order traffic flow model is proposed.Synchronization criterion is obtained by the synchronous controller,which is designed by using the parameter adaptive method.Through the numerical simulation,the correctness and feasibility of the theory are ver-ified.The second part mainly studies the synchronization problem of two continuous systems with different dimensions,taking into account the external interference and sys-tem uncertainty.Firstly,feedback control and sliding mode control are used to make the system synchronize in finite time.Comparing the two theories we can concluded that the sliding mode control has better robustness to external disturbance.Secondly,since con-vergence time will increase gradually with the increase of initial value in the finite time synchronization method,that is,the convergence time depends on the initial value,there-fore the fixed-time synchronization problem is studied in this article.The convergence time has an upper bound and will not increase continuously with the change of initial value using the fixed-time synchronization method,which is more useful than finite-time synchronization in reality.In the numerical simulation verification section,the Lorenz chaotic system and the Lorenz hyperchaotic system are taken as examples to verify the feasibility of the finite-time synchronization and fixed-time synchronization theory for d-ifferent dimensions,and the superiority of the fixed-time synchronization is also proved.The next organization of this article is as follows:The first chapter summarizes the work of this paper,illustrates the research status,the main content and the innovation of the paper's research methods.In the second chapter of this dissertation,the discrete-time traffic flow model of frac-tional order is proposed.The dynamic properties were studied,the synchronization cri-terion is deduced by using the parameter adaptive method.The dynamic nature and the synchronization effect diagram are verified to verify the correctness and feasibility of the theory.The third chapter mainly studies the synchronization of two continuous systems with different dimensions,and considers external interference and system uncertainties in the system study.First,by comparing the finite-time synchronization of sliding mode control and the limited time synchronization of feedback control,it can be proved that the sliding mode control is more robust to disturbances.Second,In order to overcome the limitations of the finite-time convergence depending on the initial value,this paper also studied the fixed-time synchronization problem of sliding mode control.finally,the correctness and feasibility of the theory is verified.The fourth chapter summarizes the work of this paper,and forecasts the next work.