本論文提出一種創新的方法論以建構小波轉換域中的預測型濾波器及其在影像插值方面的應用。首先，針對具有干擾之未知非線性系統，創新地提出一種以基於最佳誤差補償疊代學習觀測器為基礎的標的輸出-標的控制輸入追蹤器。此部分的原創性包括下列創新主題：一、適用於具有系統及輸出干擾項之類比系統的線性二次最佳化類比型標的輸出軌跡追蹤器；二、適用於具有系統及輸出干擾項之資料採樣系統(即類比系統配數位控制器與零階訊號保持器)的數位重新設計線性二次最佳化數位型標的輸出軌跡追蹤器；三、針對具有未知的系統及輸出干擾項之重複運作式類比系統所提出的反覆式學習二次最佳化類比型標的輸出軌跡追蹤器；四、針對具有未知的系統及輸出干擾項之重複運作式資料取樣系統所提出的反覆式學習二次最佳化數位型標的輸出軌跡追蹤器；五、適用於具有系統及輸出干擾項之數位系統的線性二次最佳化數位型標的控制輸入暨標的輸出軌跡追蹤器；六、針對具有未知的系統及輸出干擾項之重複運作式數位系統所提出的反覆式學習二次最佳化數位型標的控制輸入暨標的輸出軌跡追蹤器；七、適用於具有系統及輸出干擾項之類比系統的線性二次最佳化類比型觀測器；八、適用於其具有系統及輸出干擾項之資料採樣系統的數位重新設計線性二次最佳化數位型觀測器；九、針對具有未知的系統及輸出干擾項之重複運作式類比系統所提出的反覆式學習二次最佳化類比型觀測器；十、針對具有未知的系統及輸出干擾項之重複運作式數位系統所提出的反覆式學習二次最佳化數位型觀測器；十一、上述方法的延伸：從給予的已知線性系統至具有時間延遲之未知非線性系統。本論文同時呈現出上述方法在自動控制領域上的應用。其次，整合上述創新提出的方法，另一種創新的方法論，以建構小波轉換域中的預測型濾波器及其在影像插值方面的應用，亦在本論文中首度被提出，所提方法的特性亦於本論文中被詳加探討。相關例題展現了本文所提方法的有效性。

A novel methodology for constructing prediction filters in wavelet-transform domain and its novel application to image interpolation is proposed in this thesis. Firstly, a novel optimal error compensation iterative learning observer-based tracker for the unknown nonlinear system with disturbances is proposed. The novelty in this part includes the following newly presented items: 1. a new optimal analog tracker design for the continuous-time system with known disturbances, 2. a new digital-redesign linear quadratic tracker (LQT) design for the sampled-data system with known disturbances, 3. a new iterative learning LQT design for the repetitive continuous-time system with unknown disturbances, 4. a new iterative learning LQT design for the repetitive sampled-data system with unknown disturbances, 5. a new LQT design for the discrete-time system with disturbances, 6. a new iterative learning LQT design for the repetitive discrete-time system with unknown disturbances, 7. a new analog linear quadratic observer (LQO) design for the continuous-time system with known disturbances, 8. a new digital-redesign observer design for the sampled-data system with known disturbances, 9. a new iterative learning analog LQO design for the repetitive continuous-time system with unknown disturbances, 10. a new iterative learning digital LQO design for the repetitive discrete-time system with unknown disturbances, and 11. an extended applications of above design methodologies from the given linear systems to the unknown nonlinear system with input time delay. Applications of the above mentioned design methodologies on the automatic control area are also given in this thesis to demonstrate their novelty. Secondly, integrated with the above newly presented methods, another novel methodology for constructing prediction filters in wavelet-transform domain and its novel application to image interpolation as well as more detailed study on its characteristics are presented. Corresponding illustrative examples are also given in this thesis to demonstrate their effectiveness.

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