本博士論文提出了數個狀態觀測器(也稱為軟感測器)設計方法，均可達成以下兩點: (i)指定狀態觀測器之特徵值以滿足期望的收斂性能或使得狀態估測誤差快速收斂到零；(ii)可最小化估測值與實際狀態間之偏差的二次性能指標，以減少觀測之暫態估測誤差。藉由結合正交函數方法和智能進化優化演算法的優點，本論文研究了基於可觀測形式動態系統的降階觀測器和狀態延遲系統的全階觀測器的設計問題。對於基於可觀測形式的動態系統，當輸出的數量大於要估測之狀態的數量時，本論文所提出的最優降階觀測器設計方法可用於設計觀測器的增益矩陣，而現有文獻的方法則無法做到此點。對於狀態延遲系統，基於線性矩陣不等式之條件的約束可使狀態估測誤差漸近收斂到零，從而減少穩態誤差，此外本論文所提出之具二次性能指標的全階觀測器設計方法針對暫態誤差給出懲罰，從而改善了狀態延遲系統的觀測器之暫態誤差性能。藉由求解Sylvester方程式並融合正交函數方法和智能進化優化演算法，本論文也研究了基於非可觀測形式動態系統之降階觀測器的設計問題；該基於非可觀測形式動態系統設計所獲得之降階觀測器，其估測狀態可以直接用於狀態回饋控制。本論文所提出之新穎設計方法可避免相關文獻中現有方法之缺點。從示範例中可以看出，本論文所提方法之狀態估測誤差快速收斂到零，並且其性能指標值明顯優於基於現有非最優設計方法的設計結果。

Several new methods have been proposed in this dissertation to design state observers (also called soft sensors) such that (i) the eigenvalues are specified to satisfy desired convergence performance or the state estimation errors quickly converge to zero, and (ii) simultaneously, a quadratic performance measurement of the deviation of estimates from the actual states is minimized for reducing large error during the transient period of observation. By combining the merits of both the orthogonal functions approach (OFA) and intelligent evolutionary optimization (IEO) approach, both the design issues of reduced-order observers for observable-form-based linear time-invariant dynamical systems and full-order observers for linear time-invariant state-delay systems have been studied. For observable-form-based dynamical systems, the proposed optimal reduced-order observer design method can be used to uniquely determine the observer gain matrix when the number of outputs is greater than the number of states to be estimated, whereas existing approaches fail to do so. For state-delay systems, the constraint of the linear-matrix-inequality-based condition makes the state estimation errors asymptotically converge to zero so that the steady-state errors are reduced. Furthermore, the proposed full-order observer design method with the quadratic performance measurement gives a penalty for the transient error to improve the transient error performance of state-delay systems. By solving a Sylvester equation and by fusing the OFA approach and the IEO approach, the design issue of the reduced-order observer for non-observable-form-based linear time-invariant dynamical systems has also been studied. The estimated states obtained from the designed non-observable-form-based-reduced-order observer can be directly used for state feedback control. These proposed new design methods can avoid the shortcomings of existing approaches in relevant literatures. From the demonstrative examples, it can be seen that the state estimation errors of the proposed approaches quickly converge to zero and their performance measurement values are apparently much better than those based on the existing non-optimal design methods.

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