基於三維度Rabinovich微分系統，本論文重新設計出一個新四維度Rabinovich超渾沌系統。然後運用各種技術分析此新系統，為了使我們更了解此新系統的特性。此外，我們將此系統以電路模擬軟體Multisim呈現，接著在電路板上建立實際電路，藉此與模擬結果作比較。
在控制部分，為了使此新系統之動態行為及控制結果能實現在數位訊號處理器(DSP)上，此系統須作離散化。接著，設計一個狀態回授控制器使其動態能達到穩定，同時，為了達到成本效益，我們嘗試將控制器數目從原先的四顆逐次減少至一顆。模擬及實驗結果顯示只使用一顆控制器比使用四顆控制器不僅減少了控制器成本，且平均收斂時間也有2.43%的改善。
最後，我們討論基於新四維度Rabinovich超渾沌系統而設計出的分數階Rabinovich渾沌系統。先以分數階穩定準則及分歧圖來分析此分數階系統，然後基於此穩定準則設計出非線性回授控制器使兩個不同初始值的分數階渾沌系統能達到同步。此外，我們也以實際電路板呈現渾沌的同步結果進而驗證控制器的設計理論。

Based on 3D Rabinovich differential system, this thesis is dedicated to re-design and produce a new 4D Rabinovich hyper-chaotic system. Several techniques were used to analyze the proposed system in order for us to better understand the characteristics of the proposed system. In addition, the proposed system is performed by circuit simulation software Multisim, then, an actual circuit is realized on the electronic circuit board in order to compare with the simulated results.
In the part of control, in order to make dynamical behaviors and control results of the new system can be implemented on a digital signal processor (DSP), the designed new system must be discretized. Next, a state feedback controller is designed to stabilize the hyper-chaotic motion, at the same time, we try to reduce the number of control inputs from four to one in order to achieve the cost-effectiveness. The simulated and experimental results show that the controlled system with only one controller not only reduce the cost of the controller but also achieve an improvement of 2.43 % in average convergence time than the system with four controllers.
Finally, the fractional-order chaotic system is designed and studied based on the new 4D Rabinovich hyper-chaotic system. First, the stability criteria and bifurcation diagram are used to analyze the proposed system, and then a nonlinear feedback controller is designed according to the stability criteria to synchronize two fractional-order chaotic systems with different initial conditions. Furthermore, chaotic synchronization is also implemented on the actual circuit board in order to validate the designed method.

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