Study On Some Problems Of Chaos Control And Synchronization

Chaos is a very complex motion with definite stochastic rules and a final bound in nature. In recent years, chaos is widely applied to engineering, intelligent information processing, computational science, communications, life sciences, socio-economic areas and so on. The control and synchr- onization of chaos become a hot issue of study in nonlinear science. However, the theories of control and synchronization for chaos systems are not perfect enough. The methods for the control and synchronization of chaos systems need to be further investigation, for example, to design simple and effective controllers. In this thesis, some problems in control and parameter identification of chaos systems are studied. The main work and research results are as follows:1. Due to the limitations of physical devices, there exists the inevitable interference in linear input so that causes the linear input into the nonlinear input. Using sliding mode control, The proof of the chaotic systems to be realized stable under the effection of two different dirturbance (ie, matched the external dirtuebance and unmatched external dirturbance) is strictly proved. It improves and extends the results in existing literature that only to discuss the case that no disturbance or matching external disturbance and get more general conclusions.2. According to the concept of second-order sliding mode and the stability theory of Lyapunov function, the stabilization for a class of chaotic systems with unmatiched external disturbances is investigated. Using non-sigular second-order sliding mode control approach, makes the state of chaotic system converge to the neighborhood of the equilibrium point and the chattering phenomenon has been eliminated. Numerical simulations show its better than the existing method of some literatures.3. By introducing a nonlinear state feedback controller into a three-dimensional chaotic system to produce a new 4D system. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. This can verify the system has hyperchaotic behavior. Feedback control and implusive control approaches are employed here to stabilize the new hyperchaotic system.4. Discuss the modified projective synchronization of chaotic systems under two conditions, one is that the chaotic systems suffers parameter uncertainty, external disturbance and dead-zone nonlinear input; the orther is that the disturbances of chaotic systems generate the unknown exogenous systems. The corresponding numerical simulation show the effectiveness of proposed methods.5. Discuss a class of chaotic systems with transimitted signal. Based on the concepts of observer and adaptive H_∞synchronization, taking the transimitted signal as an external system state and designing an observer by using the measured output to estimate the state and transimitted signal. By setting the suitable conditions to reduce the influence of the external disturbance and unknown parameters so that estimation error of the observer can achieve adaptive H_∞synchronization. Then, the transmitted signal can be estimated.6. A summary is given and some problems are pointed out for further research.