基於李亞普諾夫穩定度理論，我們針對具有擾動的大型系統提出具有干擾機制之分散式適應性步階迴歸追蹤控制器以解決追蹤問題。受控系統的動態方程式比起純回饋形式更為寬廣。首先將受控系統轉換成具有半嚴格回授的動態系統，且根據步階迴歸控制法則設計分散式追蹤控制器，使得受控系統的輸出可以追蹤到參考訊號。此外，在控制器中加入了適應性與干擾估測機制，其優點分別為對於系統的干擾跟互聯項的上界可不必事先知道，且不須對虛擬控制輸入作微分，以避免設計的過程過度的複雜。另外還可解決動態平面控制(DSC)初始值不能隨意挑選的問題。這樣不僅能保障整個大型系統的穩定度，而且其追蹤的精準度也可以藉由設計的參數來調整。最後本論文提供一個數值範例和一個實際應用來驗證本控制器的可行性。

Based on the Lyapunov stability theorem, a decentralized adaptive backstepping tracking control with perturbation estimation scheme is proposed in this thesis for a class of perturbed large scale systems to solve tracking problems. The dynamic equations of the plant is more general than those in the pure feedback form. We first transformed the dynamic equations of the plants into a semi-strict feedback form, then designed the controllers by using backstepping control method, so that the outputs are able to track the reference signals. In addition, perturbation estimation mechanisms are employed so that there is no need to compute the derivatives of the virtual input functions, and the upper bounds of the perturbations as well as perturbation estimation errors are not required to be known in advance either. Therefore, the problems of “explosion of complexity” are totally eliminated. The resultant control scheme guarantees the stability of the whole controlled systems, and the tracking precision can be adjusted by tuning the design parameters. Finally, a numerical example and a practical example are demonstrated to verify 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 . . . . . . . . . . . . . . . . . . 4
Chapter 2 Design of Adaptive Backstepping Controllers with Estimators 5
2.1 System Descriptions and Problem Formulations . . . .5
2.2 State Transformation and Partition . . . . . . . . . . . . . . . . .8
2.3 Design of Decentralized Controllers . . . . . . . . . . . . . . 11
2.4 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
2.5 Design of Decentralized Controllers with Perturbations Estimators embedded in virtual inputs and control inputs . . . . . . . . . . . . . . . . . 26
2.6 Stability Analysis: Perturbation estimators are employed in virtual inputs and control inputs . . . . . . . . . . 33
Chapter 3 Numerical Example 38
3.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
3.2 Practical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Chapter 4 Conclusions 82
Bibliography 83
Appendix A 89
Appendix B 92

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