Controlling Chaos in a Noisy Chaotic System

• Main Authors: Kuan-Yu Chen, 陳冠宇
• Other Authors: Pi-Cheng Tung
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/5vh689

博士 === 國立中央大學 === 機械工程研究所 === 96 === Independent component analysis (ICA) is a signal processing and statistical method designed to separate independent sources given only observed or measured data that are mixtures of some unknown sources. These unknown sources are assumed to be non-Gaussian and mutually independent. In addition, controlling chaos of chaotic nonlinear systems has been received much attention and becomes more important for many industrial applications. Furthermore, chaos synchronization between master and slave chaotic systems has been attractive topic for its potential applications for secure communications. State feedback control for canceling disturbance and nonlinearity of control systems has been systematic and well developed. In this dissertation, based upon these techniques as mention above, a new scheme has been proposed to combine the ICA method for separating chaotic signals from measured white noise with a state feedback control for cancelling nonlinearity of chaotic system. In this study, we first develop a systematic procedure of state feedback control, based on a Lur’e-type system, to analyze the synchronization of two chaotic systems in the presence of random white noise. With the aid of the proposed modified independent component analysis, the real chaotic signal can be extracted from a noisy source where the chaotic signal has been contaminated by random white noise. The synchronization time can be arbitrarily designed to guarantee stability, even if the system’s output is corrupted by measurement noise. Secondly, we combine a modified independent component analysis approach with an approach for feedback cancellation of nonlinear terms. This approach to engineering control can be utilized to efficiently govern a noisy chaotic system. The methodology is easy to comprehend and to implement, but previous knowledge of the system dynamics is needed. Two examples are provided to show the effectiveness of the proposed scheme. Finally, the results of the thesis demonstrate the fruitfulness of the state feedback and the ICA theory application to the synchronization and control problems for noisy chaotic systems. The new scheme is first used for control systems with measurement noise which can replace the conventional Kalman filter.