Research On The Control And Synchronization For Uncertain Chaotic Systems

Chaotic control and synchronization is important research branch of chaos. Nearly half a century, with the rapid development of nonlinear science, research and application of chaos theory has become the main direction of complex nonlinear scientific. Some subjects are very worthy of study, such as how to control the chaotic motion effectively, how to make two chaotic (hyperchaotic) systems to achieve synchronization, and how to utilize the chaotic synchronization method realizing complex network synchronization, etc.The paper introduces some basic concepts of chaos, including the formation and development of chaos theory, the origin, present, and typical models of chaotic control and synchronization, and then proposed the chaotic (hyperchaotic) systems control and synchronization. Finally, the self-adaptive synchronization of complex network is studied and the Adaptive coupling strength algorithm is developed. Specific studies are summarized as follows:1. The Fuzzy Neural Control of chaos is studied, and an adaptive fuzzy neural controller for a class of unknown chaotic system is developed, the controller consists of fuzzy neural controller and robust controller. The fuzzy neural controller consists mainly of a fuzzy neural network identifier, by adjusting the parameters of fuzzy neural network to achieve the estimates of the controlled system. Gaussian function is widely used radial basis function, therefore, the adjustment parameters include the connection weights after the piece parts, and the antecedent part of the Gaussian membership function of the mean and variance, the application of BP algorithm to adjust these parameters online. Robust controller guarantees the stability of the controlled system and achieves the desired control performance. Finally, the simulation results further demonstrate the effectiveness of the program.2. The synchronization problems of a unified haperchaotic system over the known and unknown parameters are studied. Firstly, Based on Lyapunov stability theory, an adaptive controller is developed by the adaptive full state hybrid projective synchronization method, and theoretically proved the known parameters of the controller can achieve the unity of the whole state of super hybrid chaotic system map synchronization. Secondly, a synchronous controller is developed by the active control to achieve the unified hyperchaotic system synchronization. The third argument is the unknown chaotic system under a unified hyperchaotic adaptive control and anti-synchronization. Adaptive controller was designed to prove that the controller can make a unified hyperchaotic system with unknown parameters asymptotically stable in the fixed point. Adaptive anti-synchronization controller is designed to achieve a unified haperchaotic system with unknown parameters of the complete synchronization. Numerical simulation results further validate the effectiveness of the proposed scheme. 3. The adaptive synchronization of haperchaotic systems with parameter perturbations is studied. Based on Lyapunov stability theory, an adaptive controller is designed, which proved theoretically that the self-synchronization of the hyperchaotic Qi system can be achieved with parameter perturbations, and the different structure synchronization of the hyperchaotic Qi system and hyperchaotic Lorenz system. Finally, the simulation results further validate the effectiveness of the proposed scheme.4. The rule coupling complex network self-adaptive synchronization is studied, firstly, the coupling strength algorithm is developed, which can stabilize effectively and synchronize the complex network, and secondly, the algorithm is strict proofed from the view of mathematics. Particularly, the complex network synchronization is determined by coupling strength completely. Finally, through an example, take the Lorenz system as the complex network nodes, further verified the effectiveness of the proposed algorithm.