旋轉支點單擺之渾沌同步與反控制

Abstract

本篇論文主要探討旋轉支點單擺系統之渾沌同步與反控制。首先運用外加不同的耦合項與observed-based的方法，使得兩個不同初始值的渾沌系統達到同步，並藉由相平面圖、李亞普諾夫指數、龐加萊映射法、同步時間來做驗證。再利用歐幾里得幾何距離畫出同步系統單向耦合強度與距離的關係圖，並分析初始值與耦合強度對系統暫態的行為的影響。接著在渾沌同步應用方面，利用渾沌系統的狀態變數作為加碼與解碼函數變數，並模擬完成整個秘密通訊系統。在渾沌反控制部分，以外加控制項包括常數項、週期函數、週期脈衝、時間延遲以及適應控制，使原本為週期行為的系統控制到渾沌行為、並由李亞普諾夫指數以及分叉圖來驗證其控制結果。

Chaos synchronization and anticontrol of a rotationally supported simple pendulum studied in this thesis. Different kinds of coupling terms are used to synchronize the two identical chaotic systems with different initial conditions. An observed-based scheme is also used to achieve synchronization. The results are demonstrated by phase portrait, Lyapunov exponent, Poincaré maps and synchronization time. Next, in order to analyze the transient behavior of the synchronized systems, Euclidean distance is used to plot a figure with coupling strength versus the distance. The chaotic signals are used to mask the message function in the secure communication system. Finally, anticontrol of chaos is achieved by adding constant term, periodic term, impulse term, time-delay term and adaptive control.