根據渾沌理論，我們設計了一個四維度渾沌系統並對其特性來做分析。因此我們應用相圖分析、平衡點分析、分歧圖、龐加萊圖、李亞普諾夫指數等技術，來分析此渾沌系統的特性及其運動行為，緊接著我們討論控制理論，利用控制器讓兩個相似但初始條件不同的渾沌系統進行同步。
此論文，我們利用滑動控制來設計控制器給四維度渾沌系統讓從系統同步主系統。
雖然滑動控制可以使渾沌系統進行同步，但我們卻發現滑動控制器的效能並不是很理想。而為了提高效能，我們提出了Lipschitz滑動控制來改善效能。除此之外，我們也想要實現渾沌系統以及渾沌系統利用控制器進行同步後的結果。因為FPGA被廣泛的使用，因此我們選擇實現在FPGA上。然而在實現之前，我們必須先離散渾沌系統而我們是利用尤拉後差法對系統做離散。離散完後建立模型在FPGA上。最終，離散渾沌系統則能實現在FPGA上，而我們可以利用數位示波器對FPGA裡的渾沌訊號進行觀測並驗證。

According to chaos theory, we design the four dimensional chaotic system and analyze their properties. So, we use phase portraits, equilibrium analysis, bifurcation diagrams, Poincaré maps, and Lyapunov exponent to investigate chaotic properties and motion. After that, we discuss control theory that let two identical chaotic system with different initial conditions to synchronize.
In this thesis, we utilize sliding mode control to design controller for four dimensional chaotic system and let slave system synchronize master system. Although the sliding mode control can synchronize chaotic system, we find that sliding mode control have not perfect efficiency. In order to promote efficiency, we propose Lipschitz sliding mode control. It is a combination of sliding mode control and Lipschitz condition. Furthermore, we want to achieve the four dimensional chaotic system and synchronization of chaotic system. FPGA have been widely used, so we achieve on it. Before achieving, we must discretize chaotic system. And then, we use Euler’s backward difference to discretize the four dimensional chaotic system and synchronization of chaotic system. Finally, the discretized chaotic system is implemented on FPGA and the chaotic signals are visualized using a digital oscilloscope, validating the proposed scheme.

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