| Chaos is one of complex dynamical characteristics of nonlinear systems. It's of great importance to study chaos control since all real systems are nonlinear. Indeed, systems'parameters are usually not accurate and fixed in reality, and these parameters will change along with the external and internal conditions. Furthermore, because chaotic systems are extremely sensitive to initial values, experimental studies and numerical analysis on nonlinear systems are still not completely reliable until now. In the process of study on nonlinear systems, lots of work has been done by complicated calculation to find out the nature of nonlinear systems. These works took too much time, and we still might not obtain the accurate conclusions by the methods mentioned above. Therefore, these approaches have their limitations on solving specific engineering problems.Till now, there are many ways to control chaos and the applicable systems for chaos control are also different. In this thesis, Pyragas-type delayed feedback control method is employed for a chaos system because it can be easily applied to both continuous-time and discrete-time systems. The main purpose of this thesis is to extend the delayed feedback control method to some real nonlinear systems amd expore some effective strategies on chaos control in these systems.There are three major tasks in this thesis:(1) First, we simulate and discuss the forced Duffing system by applying the Matlab Simulink toolbox, and the Pyragas-type delayed feedback method is validated to control the chaos in this system.(2) We introduce a continuous distribution system, that is, the unified Lorenz system, to extend the application of the Pyragas-type delayed feedback, and analyze the effectsof the delayed time and feedback intensityon chaos control in different branch systems. In addition, we also study the realization of chaos control on a deep level while system parameters are changing.(3) We performed the chaos control on the unified Lorenz system under the bounded noise perturbation by the Pyragas-type delayed feedback, the effects of the control method are discussed in detail for such stochastically nonlinear system, and some effective control strategies are also presented.There are two innovations in this thesis. First, the Pyragas-type delayed feedback control method has been successfully extended to the unified Lorenz system and the chaos control of the subsystems included in the unified Lorenz system has been carried out. Second, the way of chaos control on continuously variation of the parameters is obtained during the study on the delayed feedback control. We hope that these studies can be useful in engineering applications. |
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