Linear Generalized Synchronization Of Chaos Systems Based On Adaptive Control

As a discipline, nonlinear science is widely used in various fields, and much favored by scholars. Especially, chaotic synchronization and control have been a hot topic, and with in-depth study, considerable attention has been devoted to the generalized synchronization of chaos and complex network.Firstly, we give a brief account about the research and development status of chaotic, including the definitions and characteristics of chaos, as well as the development background of chaotic generalized synchronization. Then, the dissertation mainly focuses on the linear generalized synchronization of complex dynamical network with unknown parameters, and the adaptive finite time projective synchronization for two chaos system. The main work and results are divided into two parts showed as follows:1-. The adaptive linear generalized synchronization of complex dynamical network with unknown parameters is studied. Based on Lyapunov stability theory and LaSalle invariance principle, it is proved that the complex dynamic network nodes can achieve linear generalized synchronization under some certain conditions by constructing a suitable adaptive controller, and the unknown parameters in the network can be tracked to identify. The numerical simulations demonstrate the validity and feasibility of the proposed theorem. The characteristic of the controller is that we joined an unknown parameter tracking estimation, which is one of the innovation of this paper.2, The adaptive finite time projective synchronization for a class of chaotic and hyper-chaotic systems is investigated. The adaptive controller only put on the part of error system state variables. It has been proved by Lyapunov stability theory that the error system is stable in a finite time by constructing a suitable adaptive controller. What’s more the synchronization time can be calculated in advance Numerical simulations verified the correctness of the theoretical results.