On Sampled-data Fault-tolerance Synchronization Control For Chaotic Secure Communication Systems

Chaotic motion is a complex nonlinear motion, whose trajectory of the orbits in the phase plane is very complex but not stochastic. The chaotic phenomena has been observed in a lot of real systems. The research on chaos has focused on chaotic control and application, which becomes a new research topic in nonlinear science fields now. Chaos control is necessary when the chaotic motion is produced and harmful to electrical and electrical systems. On the other hand, the dynamic properties of chaos signal such as ergodicity, aperiodicity, uncorrelated, broad band and noise-like have been proved to be useful for communication and picture crypt systems. Due to the complexity, singularity and wide application potential of chaotic dynamic systems, the research on the chaotic control and synchronization theory becomes more challenging. The main contents of this dissertation contain the synchronization of chaotic system based on sampled-data and fault-tolerance and its application in secure communication system, the main contributions are as follows:Firstly, when some control component (actuator) failures occur, the synchronization based on sampled-data between the master and slave chaotic systems is investigated. By combining the input delay theory with the free-weighting matrix, a reliable feedback controller is established. With the help of the linear matrix inequality (LMI) solvers, we can easily obtain the sampled-data feedback control law and the numerical example is provided to demonstrate the effectiveness of the results. Furthermore, based on chaotic masking scheme, the secure communication system is set up.Secondly, with the failures in master chaotic system, the synchronization control method is investigated. Taking a fault in the master system into account, with an observer-based fault estimator and a feedback controller, a new fault-tolerant synchronization scheme based on sampled-data is proposed, by which the chaotic synchronization can be achieved no matter if the fault occurs or not. The stability conditions based on LMI are obtained to achieve the fault tolerant synchronization of the chaotic systems. And the effectiveness of the proposed method is demonstrated by simulations At last, the simulation results show that this synchronization control method is useful for the chaos secure communication system.Finally, the synchronization of two systems based on sampled-data is investigated when the controller contains bias failures. With the Euler approximate discretization method, the sample-based chaos system is converted into discrete-time system. And then a synchroniza- tion controller is designed based on the LMI technique. By the synchronization control platform, the communication signals can be masked completely by the chaos signal.