本文針對具有時間延遲及非匹配擾動，且不須滿足嚴格回授形式之多輸入系統，提出一種適應迴歸控制的設計方法。控制的系統包含n個區塊的動態方程式，因此先設計前面n-1個虛擬控制器，並在最後的區塊設計步階迴歸控制器。在每個虛擬控制器和步階迴歸控制器中，加入適應性增益來估測未知干擾的上界常數，所以系統中擾動的上界可不必事先知道。此外延遲及延遲導數之上界也不須預先知道。基於李亞普諾夫穩定性理論，此系統能達到漸近穩定。最後，本文將提供一個數值範例及一個實際應用，以驗證本控制器的可行性。

In this thesis an adaptive backstepping control scheme is proposed for a class of multi-input perturbed systems with time-varying delays to solve regulation problems. The systems to be controlled contain n blocks’ dynamic equations, hence n-1 virtual input controllers are designed from the first block to the (n-1)th block, and the backstepping controller is designed from the last block. In addition, adaptive mechanisms are embedded in each virtual input controllers and proposed controller, so that the least upper bounds of perturbations are not required to be known beforehand. Furthermore, the dynamic equations of the systems to be controlled need not satisfy strict-feedback form, and the upper bounds of the time delays as well as their derivatives need not to be known in advance either. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme.

Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Design of Adaptive Backstepping Controllers 4
2.1 System Descriptions and Problem Formulations . . . . . . . . . . . . . . 4
2.2 Design of Adaptive Backstepping Controllers . . . . . . . . . . . . . . . 8
Chapter 3 Numerical Example 34
3.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Practical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 4 Conclusions 64
References 65
Appendix A 70
Appendix B 73
Appendix C 74

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