Parameter Identification And Its Application For A Class Of Chaotic And Hyperchaotic Flows

Chaos control and synchronization become hotspot of nonlinear science. But research about chaos with uncertain parameters has great deficiency. Based on the theory analysis and numerical simulation, synchronization control and parameter identification for a class of uncertain chaotic and hyperchaotic flows are fully studied in this paper. The work of this thesis is presented as follows:Firstly, considering nonlinear systems with certain parameter, the problem of chaos synchronization based on linear feedback and nonlinear feedback and mix feedback of a novel lüchaotic system were discussed in this paper. Obviously any chaos synchronization method has great localization. Then a class of nonlinear system with uncertain parameters is discussed. This paper gives a kind of control observer and its theory prove of adaptive full state hybrid improved projective synchronization. The synchronization control observer is applicable to many synchronization cases. At last numerical simulation of hyperchaotic Chen and hyperchaotic Rossler with different structure are particular presented.Secondly, considering the fact that much number cannot be detect in physics experimentation, another general parameter identification scheme is designed based on multi-resolution analysis of wavelet transformation. In theory this paper give parameter identification for any nonlinear system flows with any discretionary dimension in order to avoid cockamamie illation for idiographic system. Theory analysis and numerical simulations of Lorenz, hyper-chaotic Chen systems and a novel nonautonomuous hyperchaotic system are implemented to verify the effectiveness and feasibility of the observers to identify the parameters. For any noise signal, threshold de-noising is adopted in the wavelet coefficient with different scales. Then, we reconstruct the signal to improve the accuracy of parameter identification. The method also can be applied in chaos control and chaos synchronization. At last, combining parameter identification with nonlinear feedback synchronization, this thesis achieves identical synchronization of unsteady Chu chaotic flow. Numerical simulations are given to demonstrate and verify the effectiveness and feasibility of the proposed observer.Then, improving parameter identification method based on adaptive control, parameter adaptive law for a class of chaotic and hyperchaotic flows is designed. The improved parameter identification method has great agility and practicality by theory analysis and numerical simulation. In succession, the method is applied to chaos synchronization. Combining parameter identification and linear feedback synchronization of Chen oscillator, state error variable and parameter error gradually converge to zero state. Coherence of theory analysis and numerical simulation is realized. Finally, classes of autonomous and non-autonomous systems are researched, autonomous Liu chaos system, hyperchaos Lorenz system and non-autonomous Duffing chaos are illustrated to compare observer parameter identification method and tracking parameter identification method. Based on robustness and stability of controller the observer parameter identification is much applicable and more effective not only by computer analysis but also by theory analysis.