本論文基於李亞普諾夫理論(Lyapunov Theorem)，針對強韌追蹤之問題提出一個具有擾動估測器的最佳參考模式調適控制器。且這些系統含有時間延遲和輸入非線性的多輸入多輸出之動態系統。本控制器包含了三種形式的控制器。首先是在假設無擾動情況下之最佳回授控制器。其次為具有自動調適擾動估測誤差之上界的調適控制器。最後則為擾動估測器。本控制器將保證 uniformly ultimately boundness 的特性，並分析其中參數的特性。最後，本論文提供二個數值範例以驗証控制器之可行性。

Based on the Lyapunov stability theorem, an optimal model reference adaptive control (OMRAC) scheme with perturbation estimation is presented in this thesis to solve robust tracking problems. The plant considered belongs to a class of MIMO perturbed dynamic systems with input nonlinearity and time varying delay in the state. The proposed control scheme contains three types of controllers. The first one is a linear feedback controller, which is an optimal controller if there is no perturbation. The second one is an adaptive controller, it is used for adapting the unknown upper bound of perturbation estimation error. The last one is the perturbation estimation mechanism. The property of uniformly ultimately boundness is proved under the proposed control scheme, and the effects of each design parameter on the dynamic performance is analyzed. Two numerical examples are given for demonstrating the feasibility of the proposed methodology.

Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . 3
Chapter 2 Optimal Model Reference Adaptive control 4
2.1 System Descriptions and Assumptions . . . . . . . . . . . . 4
2.2 Design of Optimal Control for a Nominal System . . . . . . 7
2.3 Design of Robust Tracking Controller with Perturbation Estimation . 10
2.4 Analysis of Stability . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Summary of Design Procedure . . . . . . . . . . . . . . . . . 18
Chapter 3 Simulations 19
Chapter 4 Conclusions 40
References 41

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