本論文針對非線性資料取樣系統提出一個具有高效能追蹤的高階反覆學習追蹤器。藉由高階反覆學習控制機制和具有高增益特性的軌跡追蹤器做結合，此新的演算法則可以減少學習收斂代數和達成更有效的數位軌跡追蹤。針對非線性系統，首先，在每一代裡面，類比非線性系統所轉換的最佳線性化模型會被架構在每一個取樣時間上的操作點。然後，為了在這個最佳線性化模型裡設計一個類比追蹤器，具有高增益特性的線性二次式調節器技術會被應用在高階反覆學習控制器的初始輸入上。這個具有高增益特性的控制器能抑制系統的不確定性誤差，像是模型化的誤差、非線性擾動和外在的干擾。因此，系統的輸出能在很短的時間內快速又準確地追蹤到所設計的軌跡。值得注意的是反覆學習控制器的初始控制輸入會直接影響誤差收斂速度。為了實用的考量，類比線性二次式調節追蹤器會先被利用數位再設計的技術做轉換，然後發展一個新的微分型高階反覆學習控制演算法來應用在非線性資料取樣系統。最後，利用數個多輸入多輸出的例子來說明本論文所提出方法的效果和可行性。

In this thesis, a novel high-order iterative learning tracker is proposed to resolve the output tracking problem for the nonlinear sampled-data system. The newly developed high-order iterative learning control (ILC) method and the high-gain property tracker design methodology are combined to significantly reduce learning epochs and find the more efficiency digital tracker. For the nonlinear system, the optimal linear model of the analog nonlinear system will be constructed at every sampling time at each iteration by taking the operating state. Thereafter, the linear quadratic regulator (LQR) design technique, with a high-gain property, is applied as the initial control input of high-order ILC to design an analog tracker of the optimal linear model. The high-gain property controllers can suppress the uncertain errors such as modeling errors, nonlinear perturbations, and external disturbances. Thus, the system output can quickly and accurately track the desired reference in a short time interval. Notice that the convergence of ILC is directly influenced by the initial control input. For practical consideration, the introduced linear quadratic analogue tracker (LQAT) is implemented by adopting the prediction-based digital redesign technique to develop a novel D-type high-order ILC algorithm for nonlinear sampled-data systems. Finally, multi-input multi-output (MIMO) numerical examples are presented to illustrate the effectiveness and the feasibility of the proposed method.

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