Control And Synchronization Of Chaotic Systems And Applications In Secure Communication

Chotic motion is a complex nonlinear motion,whose trajectory of the orbits in the phase plane is very complex but not stochastic.The chaotic phenomenon have been observed in a lot of real systems and the research on chaos has been focused on chaotic control and application now.Chaos control is necessary when chotic motion is produced and harmful to electrical and electronical systems. On the other hand, the dynamic properties of chaos signal such as ergodicity,aperiodic,uncorrelated,broad band and noise-like have been proved to be useful for communication and picture encrypt systems and in describing and diagnosing nonlinear dynamic systems.The complexity , singularity and wide potential application of chaotic dynamic systems make the research on the chaotic control and synchronization theory to be more challenging.The research of the field becomes a new research focus in nonlinear science fields.The main content of this paper contains the analysis on control and synchronization of chaotic systems and the application in secret communication.The control theory of chaotic dynamical systems mainly contain the Lyapunov Exponents-based control and open-plus-closed-loop control of discrete-time chaotic systems.The synchronization of chaoic and hyperchaotic system have been attained by several methods,which are failed into two strategies: linear feedback and observer-based synchronization. The comprehensive overview of secure communication based on chaotic synchronization and the application of chaotic synchronization in secure communication are presented in this paper. In this dissertation,the main contributions are following:1. The research on control of chaotic systems based on Lyapunov Exponents.It is proved that chaotic systems could be controlled by changing the Lyapunov exponents of the systems and setting it to be negative. The controlling area in which systems can be controlled is proposed. The simulation results show that this method is effective. 2.The research on open-plus-closed-loop control (PAOPCL). First, the open-plus-closed-loop control (OPCL) is recalled, and the condition is presented, in which OPCL can control the chaotic system when the parameters can be obtained directly.A new chaos control method, the parametric adaptive open-plus-closed-loop control, is developed for stabilizing the discrete chaotic system, in which parameters are uncertain and can not be directly measured, by estimating the real parameters using double observers. Finally, the effectiveness of the proposed approach is illustrated by stabilizing the chaotic dynamics of the Logistic map and the Henon map.3. The resarch on synchronization of chaotic systems based linear feedback strategy. Two feedback synchronization methods are presented. In the first method, based on the Lyapunov stabilization theory and nonlinear linearization theorem, a simple generic criterion is derived for synchronization of two coupled hyperchaotic systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems.By parameter adaptiving law, synchronization of hyperchaotic systems with uncertain parameter is achived.The second method is based on time-delayed bidirectional coupling.A new synchronization method of chaotic systems based on time-delayed feedback is presented, in which it is assumed that linearly coupling coefficients between two chaotic systems are identical. Based on the Lyapunov stability theory, the generic criterion is derived for global synchronization of two identical chaotic systems with time-delayed bidirectional coupling. By appropriately selecting the coupling parameters which can be obtained by solving Riccati equation, the synchronization and stability of overall systems can be guaranteed. Numerical simulations show that chaotic systems can be synchronized and by changing delay time of control signal, the system can be controlled to the fixed point or the period orbits.4. The resarch on the nonlinear observer-based synchronization of hyperchaotic systems with uncertain parameters. The observer-based synchronization theory is studied thoroughly and two methods have been proposed.The first method is the observer-based synchronization of some special discrete hyperchaotic systems with uncertain parameters. The gain matrix and adaptive law are gived.The validity of the scheme has been verified by the simulation and application of communication system using Generalized Henon system.The second method is the observer-based synchronization of hyperchaotic systems with nonlinear terms satisfying Lipschitz conditions.The Lyapunov approach was utilized to stabilize the synchronization error and new stable conditions were constructed.based on the conditions, coupling gains were designed through solving a set of linere matrix inequalities.5. Three main message encoding schemes based on chaotic synchronization were developed: chaotic masking, chaos shift keying and chaos modulation.The feasibility of the communication scheme in high-dimensional chaotic systems, such as the hyperchaotic system, is demonstrated. Numerical results show the success in transmitting figure and sound signal through chaotic systems and hardware is designed according to above approach.