Research On Control And Application Of Several Classes Of Chaotic Systems

Research on chaos is one of the important achievements in nonlinear science. Chaotic motion is a complex motion, whose equation is certain but the trajectory of the orbits is stochastic. There are lots of chaotic phenomena in real world. For oddities of chaos, uncontrolled chaos will not be applied, so chaos control is the first step of chaos application. Chaos control and cha0os application have already become hot field in nonlinear science.This project is supported by National Science Foundation of China and Hebei Science Foundation. Along the chaos control(narrow sense) and chaos synchronization, the main results of this thesis are expressed as follows: (1)By backstepping method, the strict-feedback chaotic system with uncertainties was stabilized, in which we applied continuous function and RBF neural network to compensate the uncertainties. The control aim was realized. Based on special sliding-mode control with parameter identification, the unified chaos was led to unstable equilibrium point.(2)Chaos identical synchronization and linear generalized synchronization was studied. Firstly we divided the chaos with perturbation into two parts, furthermore denoted the perturbed part by unperturbed part and output. Secondly by two nonlinear observers we realized the chaos identical synchronization. At the same time, according to unknown input linear observer, the linear generalized synchronization controller was designed.(3)For the first time, the resilient synchronization was put forward. The uncertainties or perturbation not only exist in chaos itself but also in controller, namely the controller can't be implemented exactly, which may be deadly to synchronization. To solve the problem, we design the resilient controller under known and unknown disturbed bound.(4)Chaos application in secure communication was introduced. Based on VC++, we developed image encryption software, in which chaos masking and chaos image permutation was adopted. Simulation results showed that the software implemented quickly and encrypted highly.