摘要

本文提出三個研究的主題， ( i ) 數位再設計的方法應用於混沌系統的同步化追蹤控制中。基於李亞諾夫的方法，在連續時域中，單一狀態變數的控制器被推導出。於離散時間的控制中，一種有效的數位設計的技術被提出來達成同步化兩個對等的混沌系統。( ii ) 一種改進穩定度的分析的方法被提出。穩定度準則證明假如系統存在漸近穩定態的操作點 (平衡點)，則所輸入的控制訊號所產生的軌跡仍然會趨近於漸近穩態。藉著使用最佳線性化模式，這種模式所導出實際的線性化模式於操作點中，而這些操作點所產生的解即為最佳線性化解於取樣的瞬間。( iii ) 非線性的混合模式系統具有輸入延遲的問題，以次佳化的數位再設計的方法將會被有效來控制。此外，以基因演算法則應用於數位控制器的參數調節於最佳化中。最後，數值模擬的效果則說明本文所提出的設計方法。

In this thesis, three issues are studied.
( i ) A digital redesign method is proposed for synchronizing chaotic systems. Based on the Lyapunov stability theory, a single-state variable feedback controller is derived in continuous-time domain. In discrete-time control, an effective digital redesign technique is proposed to achieve the state synchronization of two identical chaotic systems. ( ii ) An improved stability analysis for a nonlinear hybrid system is presented. The proposed stability criterion shows that if the system possesses a manifold of exponentially stable constant operating points (equilibria) corresponding to constant values of the input signal, then the input signal yields a trajectory that remains close to exponentially stable state. By using the optimal linearization method, it yields exact local linear models at operating states of interest and optimal local linear models in the neighborhood of operating states of interest. ( iii ) By using the sub-optimal digital redesign method, the nonlinear hybrid system with input time delay will be effective to control. Besides, the sub-optimal digital redesign technique uses the genetic algorithm for parameter tuning in optimization. Finally, numerical simulations demonstrate the efficacy via the proposed design methodologies in this thesis.

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