不確定超混沌系統的控制器策略及同步化設計

Control Strategy and Synchronization of Uncertain Hyper-chaotic Systems

吳瑾祈(Jin-Chi Wu)

指導教授 ： 孫永莒

義守大學/電機資訊學院/電機工程學系/碩士(2017年)

摘要

在本篇論文中，首先提出實用指數穩定化的觀念，緊接著針對一類超混沌控制系統，結合類里亞普若夫理論及微分積分不等式，提出兩套線性控制器，促使上述系統達成全域指數穩定的標的。由於所設計的控制器為線性控制器，故其可經由電子電路來實現。另一方面，吾人擬提出ε-δ 同步化的概念﹝註：ε為收歛半徑，δ 為收斂速率﹞，並針對一類具混合式不確定項之主僕控制系統，利用微分及積分不等式，設計一套保證上述不確定主僕系統達成ε-δ 同步化之新型追蹤控制器。此控制器不僅指數收斂速率及收斂半徑可事先安排，亦能克服系統外在之混合式不確定項。最後將提供多個數值範例，來驗證及說明主要定理的正確性。

關鍵字

超混沌系統 ； 全域指數穩定化 ； 實用指數穩定化 ； 追蹤控制 ； ε-δ同步化

並列摘要

In this thesis, the concept of practical exponential stabilizability is introduced and the stabilization for a class of hyperchaotic systems is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, two linear feedback controllers are proposed to realize the global exponential stabilization of such systems. Besides, the proposed control can be directly and efficiently realized by easy-implemented electronic circuits. On the other hands, the concept of ε-δ synchronization is introduced and the ε-δ synchronization for a class of uncertain master-slave systems with mixed uncertainties is investigated. Based on the differential and integral inequalities methodology, a tracking control is proposed to realize the ε-δ synchronization for such uncertain systems. Not only the guaranteed exponential decay rate and convergence radius can be pre-specified, but also the mixed uncertainties can be simultaneously conquered by the proposed control.Finally, numerical simulations will be given to demonstrate the feasibility and effectiveness of the obtained results.

並列關鍵字

Hyperchaotic system ； Global exponential stabilizability ； Practical exponential stabilizability ； Tracking control ； ε-δ synchronization

參考文獻

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