本論文針對含有匹配與非匹配雜訊之非線性系統分別提出三種不同的強健型控制策略。首先，第一種控制策略是針對具有半嚴格回授狀態延遲擾動的非線性系統，設計出適應性區塊步階迴歸控制器，用來解決系統校準的問題。在每一層的虛擬控制器中也有調適機制的設計，將一些不滿足嚴格回授的項次累積到最後一層並利用調適機制有效的壓制未知的擾動上界，使受控系統能夠達到漸進穩定。接著，第二種控制策略是針對具有匹配和非匹配擾動的非線性系統，設計區塊終端步階迴歸控制器，用來解決系統校準的問題。在設計控制器的過程中利用微分估測器來估測擾動，使其步階迴歸控制法則中過度複雜化與奇異點問題的兩大缺點可以一併消除，利用此控制架構，受控系統的狀態將在有限時間內達到零的效果。最後，第三種控制策略則是針對具有匹配與非匹配的兩個不同混沌系統利用適應性步階迴歸控制器設計來解決同步的問題，於此控制架構下，受控系統可以保證同步軌跡能夠達到UUB的特性。
上述三種控制架構皆以李亞普諾夫定理為理論基礎，針對本論文所提出之控制架構，利用數值範例來驗證其可行性。

Three robust control strategies are proposed in this dissertation for nonlinear dynamic systems with matched and mismatched perturbations. Firstly, a block backstepping control method is presented so that it can be directly applied to systems with multiple state delayed perturbations in block semi-strict feedback form to solve regulation problems. The terms in the dynamic equations which do not satisfy the block strict-feedback form are accumulated in the last design step and are suppressed effectively by the designed adaptive gains. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, hence the least upper bounds of perturbations are not required to be known in advance, and the property of asymptotic stability is guaranteed. Secondly, a terminal block backstepping control method is presented for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. A derivative estimation algorithm embedded in the controller is utilized to estimate the perturbations, so that the drawbacks of so-called ``explosion of complexity" and ``singularity problem" are totally eliminated. This control scheme not only has the ability of dealing with mismatched perturbations, but also is capable of driving the controlled states to reach zero within finite time. Thirdly, synchronization of two different chaotic systems with matched and mismatched perturbations by utilizing adaptive backstepping control technique is developed. The resultant control scheme guarantees the property of uniformly ultimately boundedness when solving the chaotic synchronization problems. Several numerical examples are demonstrated for showing the feasibility of the proposed control methodologies.

Contents
Abstract 1
List of Figures 5
Chapter 1 Introduction 7
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . . . . . . 12
Chapter 2 Design of Block Backstepping Controllers for a Class of Perturbed
Multiple Inputs and State-delayed Systems in Semi-strict Feedback
Form 14
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 System Descriptions and Problem Formulations . . . . . . . . . . . . . . 15
2.3 Design of Adaptive Backstepping Controllers . . . . . . . . . . . . . . . 17
2.4 Numerical Example and Practical Application . . . . . . . . . . . . . . . 31
Chapter 3 Design of Terminal Block Backstepping Controllers for Perturbed
Systems in Semi-strict Feedback Form 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 System Descriptions and Problem Formulations . . . . . . . . . . . . . . 40
3.3 Design of Terminal Block Backstepping Controllers . . . . . . . . . . . . 41
3.4 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 4 Design of Backstepping Controllers for Systems with Non-strict
Feedback Form and Application to Chaotic Synchronization 56
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Systems Description and Problem Formulations . . . . . . . . . . . . . . 57
4.3 Design of Adaptive Backstepping Controllers . . . . . . . . . . . . . . . 58
4.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Chapter 5 Conclusions and FutureWorks 70
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 FutureWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Bibliography 72
Appendix 81
List of Figures
2.1 The trajectory of state variable x1. . . . . . . . . . . . . . . . . . . . . . 35
2.2 The trajectories of state variables x21 and x22. . . . . . . . . . . . . . . . 36
2.3 The trajectories of state variables x31, x32 and x33. . . . . . . . . . . . . 36
2.4 The adaptive gains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Control inputs u. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 The adaptive gains (2.29) and (2.30). . . . . . . . . . . . . . . . . . . . . 37
2.7 Control inputs u with saturation function. . . . . . . . . . . . . . . . . . 37
2.8 The trajectories of state variables x1 and x2 of chemical reactor system. . 38
2.9 The adaptive gains of chemical reactor system. . . . . . . . . . . . . . . 38
2.10 Control input u of chemical reactor system. . . . . . . . . . . . . . . . . 38
3.1 The trajectory of state variable z1. . . . . . . . . . . . . . . . . . . . . . 53
3.2 The trajectory of state variable z2. . . . . . . . . . . . . . . . . . . . . . 53
3.3 The trajectory of state variable xi. . . . . . . . . . . . . . . . . . . . . . 53
3.4 The trajectory of state variable ui. . . . . . . . . . . . . . . . . . . . . . 54
3.5 The trajectory of state variable xi. . . . . . . . . . . . . . . . . . . . . . 54
3.6 The trajectory of state variable z1(Case 6 happened). . . . . . . . . . . . 54
3.7 The trajectory of state variable z2(Case 6 happened). . . . . . . . . . . . 55
4.1 Tracking errors e1, e2 and e3. . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Adaptive gains kO1, kO2 and kO3. . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Perturbation estimation error. . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Control effort u. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Tracking errors e1, e2 and e3 (Example 2). . . . . . . . . . . . . . . . . . 68
4.6 Adaptive gains kO1, kO2 and kO3 (Example 2). . . . . . . . . . . . . . . . . . 68
4.7 Perturbation estimation error (Example 2). . . . . . . . . . . . . . . . . . 68
4.8 Control effort u (Example2). . . . . . . . . . . . . . . . . . . . . . . . . 69

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