針對具有致動器失效的某些類系統，本論文提出有效的錯誤偵測法則與容錯控制。本文涵蓋以下三個主題: 首先，針對具有致動器錯誤之非線性時變資料取樣系統，提出一種修正的卡爾曼濾波器，以有效地達到錯誤偵測。由於所提的濾波器具有高增益的特性，因此能以最佳的方式，估測大幅度變動的未知致動器衰減因子，基於此，本文中提出被動式補償致動器法則以有效地修正致動器的失效，使得受控系統在致動器失效的狀況下所設計的軌跡追蹤器，依然能有效地的追蹤原預設的軌跡，本論文利用最佳線性化技巧與數位重新設計，使得所提方法能適用到非線性時變資料取樣系統。本文第二個研究主題，則針對具有致動器失效之多個線性互聯子系統所組成的資料取樣大尺度系統，提出以參考模型為基礎之創新型分散式軌跡追蹤器，並使受控之閉迴路系統具有解耦的強健性。本文的最後一個研究主題則針對具有致動器失效之二維線性多變數隨機離散系統，提出一種改良型二維卡爾曼濾波器與一創新的二維狀態空間自調式的容錯軌跡追蹤器，達到主動式容錯控制。

This dissertation is dedicated to developing fault detection and fault tolerant control for some classes of sampled-data control systems with actuator failures via digital redesign approach. It covers three topics: First, a modified Kalman filter-based adaptive observer for the nonlinear sampled-data time-varying system with actuator failures is proposed for actuator fault detection. With the high gain property of the modified Kalman filter, it is applicable to optimally estimate a large variation of unknown decay factors of actuator failures. Based on the estimated faults, the newly proposed passive input compensation method is then able to solve actuator faults for performance recovery. In this dissertation, the optimal linearization technique is used to obtain the locally optimal linear model for a nonlinear system at each sampled state, so that the actuator fault detection and performance recovery of a nonlinear sampled-data time-varying system is accomplished. Secondly, a novel digital redesign of the analog model-reference-based decentralized adaptive tracker is proposed for the sampled-data large scale system consisting of N interconnected linear subsystems with/without actuator failures. It shows that the proposed passive fault-tolerant decentralized tracker induces a good robustness in the decoupling of the closed-loop controlled system. The decentralized adaptive controlled sampled-data system is theoretically possible to asymptotically track the desired output with a desired performance. The third topic is to propose a novel state-space self-tuning fault-tolerant control for two-dimensional multi-input multi-output linear discrete-time stochastic system with actuator failures, so that the output of the controlled system can still track the desired trajectory well.

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