The Neural Networks Approaches To The Control And Synchronization Of Chaotic Systems

The synchronization and control of chaotic systems have capacious application foreground. Many kinds of methods for synchronization and control of chaotic systems have been brought forward. However, The control theory of chaotic systems is still not perfect so far because of the complexity and particularity of the dynamic behavior in chaotic systems. Especially if the mathematic model of the system can not be actually constructed and the known formation is less, the classic control methods can not act well. Study on neural networks has made great progresses in this decade. It has been proved that the neural networks can approach any continuous nonlinear function. This specialty makes it potential to control the system which is highly nonlinear or uncertain. On the basis of summarizing the use of neural networks in the control of chaotic systems, three kinds of neural networks approaches to control chaotic system are presented. The following is the main work of this thesis:1. On the basis of generalizing the appliance of neural networks to the control of chaotic systems, the prospect of research is discussed.The main applications of neural networks for chaos control are operating as identification model or controller. Identification is the base of design for control. It is important for the control of chaotic systems to construct favorable identification model, but conventional identification methods can't do it well. Comparatively, This work can be well done by neural networks. If neural networks are trained by error signal to get the appropriate control signal, it is operating as a controller. The control methods based on neural networks can also be combined with the classic control methods. An appropriate control scheme should be selected according to the particularity of the controlled system. The amelioration of control scheme and computing way using neural networks is the emphases of research. Moreover, other networks, such as function networks, have appeared. They work on the same principle of neural networks. But they can choose different functions for hiding layer, so they can approach chaos easier.2. A method to the control and synchronization of the scalar chaotic signal is presented using neural networks with linear outputs in this thesis. We modeled the controlled chaotic systems in neural networks with linear outputs. Based on Lyapunov theory and control methods of nonlinear systems, the change law of weights of neural networks and a nonlinear feedback controller are designed. The scalar output of the model can synchronize the given scalar chaotic signal.Chaotic signal with continuous wide band frequency spectrum is not periodic and is similar with noise signal. These properties make it suitable to secret communication. The development of chaos synchronization makes it realizable to use chaos for secret communication. The crux of secret communication is the secrecy of secret key. It has been pointed out that declassification can be realized by reconstructing phase space. The method presented in this paper constructs the chaotic systems using neural networks. The scalar output of the reconstruction model can synchronize the given scalar chaotic signal. This method offers a new way to get secret key. Both theory analysis and simulation results illustrate the validity of the method.3. Neural-based observer is integrated with synchronization control of chaotic systems. Assuming that the chaotic systems can be separated into linear and nonlinear components, a neural-based observer is constructed by tracing the nonlinear components of the system using RBF (Radial Basic Function) neural networks. The synchronization control of the system is accomplished.State observer is a realizable dynamic system in practice. It is driven by the input signal and output signal of the observed system. Its output can trace the state variable of the observed system properly. Because the complexity of nonlinear system, the design of nonlinear state observer is difficult. Neural networks hav...