一般而言，要精確量測控制系統的參數有其局限，往往只能以不確定的區間數值表示。模糊參數不確定性系統(fuzzy parametric uncertain system)其不確定性參數以模糊理論的α cut (α∈[0,1])表示。α cut的表示法可將不確定性的參數輔以機率的特性，相較傳統區間數值表示法，更適合描述系統的不確定性參數。本論文分別探討二種模糊參數不確定性系統的強健控制器設計問題。
第一部分考慮非線性模糊參數不確定性油電混合動力車(HEV)系統縱向速度控制問題。首先利用最佳控制理論，將系統最大的不確定性參數區間轉換為LQT控制器設計所需的權重函數，並保證所設計的強健控制器能穩定所有不確定性系統。再利用二自由度設計觀念，搭配前項模糊補償器以滿足系統追蹤性能需求。第二部份針對非線性模糊參數不確定性癌症腫瘤系統，其不確定性的模糊參數先以樂觀度(λ∈[0,1])轉換。再推導不確定性癌症腫瘤系統漸近穩定邊界(RAS)存在的充要條件。同時利用反向及前向積分法，分析系統的3維漸近穩定邊界並驗證在不同的樂觀度的初始條件下，系統能正確反應腫瘤細胞、健康細胞與免疫細胞的消長。另針對導致暫態混沌消失的邊界危機(Boundary crisis)現象，設計非週期式自體免疫細胞輸入療法(Adoptive Cellular Immunotherapy; ACI)以避免健康細胞滅絕。
本論文所設計的強健控制器不僅可避免傳統強健控制設計問題所需較複雜的數學式，並可有效滿足系統所需的性能需求。此外創新非線性模糊參數不確定腫瘤模型更符合臨床表徵。最後所獲之結果也與其他文獻的成果相比較，並說明改進之處。

Generally speaking, the mathematical model of controlled plant exists a certain amount of uncertainty. The uncertainties are usually expressed in terms of the interval coefficients of the transfer function polynomials. For fuzzy parametric uncertain systems, the uncertain parameter can be represented by a fuzzy number with a membership function. The membership value α∈[0,1] can be interpreted as a kind of confidence degree. Comparison with traditional interval approach, the fuzzy representation can indicates the interval of variations and the possibility of variation interval simultaneously. The motivation of this dissertation focuses in the robust controller design for two kinds of fuzzy parametric uncertain systems.
First, a new robust two-degree-of-freedom (DoF) design method for controlling the nonlinear longitudinal speed problem of hybrid electric vehicles (HEVs) was proposed. The maximum uncertainty interval of the system was translated into the weighting matrix Q of the LQT problem to guarantee that the designed optimal controller was robust under worst-case conditions. Then, by using 2 (DoF) design concept, the fuzzy forward compensator was incorporated with a robust feedback controller to enhance the system tracking response. Second, a nonlinear fuzzy parametric uncertain Lotka–Volterra cancer model was considered. By using grade mean value conversion, the fuzzy biological parameters were translated into the degree of optimism (λ-integral value∈[0,1]) interval. We derived the sufficient conditions for the existence of the region of asymptotic stability (RAS) in the fuzzy cancer model. Through forward and backward integration methods, the extinction condition of the healthy and immune cell populations and boundary crisis of transient chaos were also investigated under fuzzy environment. We presented a nonperiodic ACI protocols to avoid tumor cell uncontrolled growth and prevent health cell extinction.
The advantages of the proposed approach are that it is not only intuitive but also requires modest computational effort. Besides, the nonlinear fuzzy parametric uncertain cancer model can reflect relevant clinical phenomena. The results have shown to be better improvement than those appeared in recent literatures.

Contents
Acknowledgement i
摘 要 ii
Abstract iii
Contents v
List of Figures vii
List of Tables ix
Chapter 1 Introduction 1
1-1 Motivation 1
1-2 Background and Paper Review 2
1-3 Brief Sketch of the Contents 4
Chapter 2 Mathematical Preliminaries 6
2-1 α cut Representation of Fuzzy Parametric Uncertainty 6
2-2 Kharitonov Theorem 7
2-3 The Necessary Condition about Saddle Point and RAS 8
2-4 Grade Mean Value Conversion 10
Chapter 3 Robust LQT Controller design for Fuzzy Parametric Uncertain Systems 12
3-1 Introduction 12
3-2 Problem Formulation 15
3-2-1 The Architecture of the HEV Model 17
3-2-2 Fuzzy Parametric α-Cut Representation of the Uncertain HEV Model 19
3-3 Robust LQT Controller Design 20
3-3-1 Optimal Robust Controller Design for a System with Fuzzy Parametric Uncertainty 20
3-3-2 Determination of the Uncertainty Weighting Matrix 23
3-3-3 Optimal-Based Robust LQT Feedback Controller Design 24
3-3-4 Fuzzy Logic Forward Compensator Design 25
3-3-5 Design Procedure 28
3-4 Numerical Examples 29
3-4-1 Simulation of Optimal Based Robust Feedback Controller 29
3-4-2 Simulation of 2-DoF Robust Controller 32
Chapter 4 Nonperiodic Controller Design for Fuzzy Parametric Uncertain Cancer Systems 36
4-1 Introduction 36
4-2 Problem Formulation 40
4-2-1 Three-dimensional Lotka-Volterra Crisp Cancer Model 40
4-2-2 Three-dimensional Lotka-Volterra Fuzzy Cancer Model 41
4-2-3 Equilibrium Point Analysis of Fuzzy Cancer Model 41
4-2-4 The cause of boundary crisis in cancer model 43
4-3 Sufficient Conditions for the Existence of RAS in Fuzzy Cancer Model 44
4-4 Nonperiodic Controller Design 48
4-5 Numerical Examples 50
4-5-1 Dynamical Analysis of fuzzy cancer model 50
4-5-2 Nonperiodic Control of Transient Chaos for Fuzzy Cancer Model 56
Chapter 5 Conclusions and Future Work 62
5-1 Conclusions 62
5-2 Future Work 63
Reference 65

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