Theory And Application Of Adaptive Synchronization Method

Synchronization as an omnipresent phenomenon has become a topic of im-portance in numerous fields. Among all the synchronization related topics, the chaos control and synchronization have been widely investigated and con-sequently applied in plenty of fields. Particularly, the newly developed technique based on the adaptive coupling has aroused a great amount of attention from many researchers. This thesis focuses on the theoretical analysis and practical applications of the adaptive synchronization technology for nonlinear dynamical systems. It begins with several counterexamples, showing some gaps existent in the literature. With the rigorous mathematical analysis, the relations among the global synchronization, the uniform Lipschitz condition, and the boundedness of the investigated systems are revealed. Furthermore, the linear independence condition is established novelly to guarantee a successful identification of un-known parameters in dynamical systems. In addition, the uniform Lipschitz condition is further relaxed to the local Lipschitz condition, and correspondingly the sufficient conditions for local synchronization as well as global synchroniza-tion are obtained. To accelerate the convergence speed, a nonlinear adaptive rule is proposed and tested for some representative systems with a large amount of parameters.In the second part of this thesis, various applications are discussed in light of the mechanism from the adaptive synchronization. First, the adaptive delay feedback control algorithm is designed to stabilize and retrieve those unstable periodic orbits embedded in chaotic at tractors. This algorithm is validated both theoretically and experimentally. Then as another important application of the adaptive synchronization technique, the estimation of unknown time delays as well as parameters is further investigated systematically. As for the delayed dy-namical systems that are always regarded as systems with infinite dimension, the adaptive algorithm for time delay estimation is established which is intrinsically different from the conventional algorithms for parameters estimation in ODE systems. In addition, several necessary condition or restrictions for parameters identification are considered for several real systems, such as the avoidance of the linear dependence as mentioned above, and successful identification in the case of having insufficient data. Based on the adaptive parameter estimation al-gorithms, a novel wireless chaotic digital communication framework is designed, which is investigated and tested in multiple-input multiple-output systems. Its performance test is carried out by simulations in standard wireless channel mod-els.Finally, several directions for future work are summarized.