臺灣博碩士論文加值系統

本論文針對多輸入多輸出(multiple-input-multiple-output, MIMO)非線性非仿射(non-affine)系統，提出基於遞迴式小波類神經網路(output recurrent wavelet neural network, ORWNN)之適應性控制機制:改良型適應性遞迴步階控制(improved adaptive backstepping control, IABC)與直接式適應性遞迴步階控制(direct adaptive backstepping control, DABC)。本文所提出的ORWNN結合小波類神經網路(wavelet neural network, WNN)及模糊類神經網路(fuzzy neural network, FNN)和輸出遞迴層之優點建構而成。本文考慮受控系統之系統動態函數為未知，且存在外部干擾或系統參數擾動;控制器設計中，我們首先將非線性非仿射系統，轉換成類似嚴格迴授(strict-feedback)型態，並透過ORWNN來估測未知函數，透過遞迴步階的技術，逐一設計子系統之虛擬控制器與實際之適應控制器。在IABC控制器設計中，本文結合動態滑面控制(dynamic surface control, DSC)的技巧以解決傳統遞迴步階控制的劇增變動複雜度(explosion of complexity)問題；根據ORWNN估測的結果， IABC 的控制輸入可藉由遞迴步階控制的概念設計，且藉由李亞普諾夫定理推導，可獲得網路參數的適應法則，並保證系統閉迴路穩定且追蹤誤差為全域最終均勻有界(UUB)。在DABC 控制器設計中，理想的虛擬控制器及實際控制器以ORWNN近似，並設計強健控制器補償近似誤差，並基於李亞普諾夫定理推導，並保證系統閉迴路穩定。最後，我們將提出的IABC與DABC，應用於二階、三階多輸入多輸出非仿射非三角系統、雙單擺(double-pendulums)、雙台車型倒單擺 (inverted double pendulums on cars)、二自由度直昇機(2-DOF-helicopter) 、機械臂控制 (robot arm control) 系統上，由模擬結果可驗證所提出的控制系統，均能達到令人滿意的控制性能。

This thesis proposes two adaptive backstepping controllers for a class of multi- input-multi-output nonlinear uncertain non-affine systems via output recurrent wavelet neural networks (ORWNNs). The proposed ORWNN combines the advantages of wavelet-based neural network (WNN), fuzzy neural network (FNN), and output feedback layer. Before designing the adaptive controllers, we first transform the non-affine system in non-triangular form into strict-feedback-like form. The ORWNNs are used to estimate the unknown functions for developing the adaptive backstepping controller. The proposed adaptive backstepping controller combines the concept of dynamic surface control (DSC) technique to treat the major drawback of backstepping “explosion of complexity”, called ORWNN-based improved adaptive backstepping control (IABC). Based on the Lyapunov approach, IABC guarantees that system output converges to a small neighborhood of the reference signals, i.e., the tracking errors are globally uniformly ultimately bounded (UUB). Additionally, the direct adaptive backstepping control scheme using ORWNNs is developed, called DABC. The ideal virtual controllers and actual controller are approximated by ORWNNs. The corresponding robust controller is designed to compensate the approximated error of ORWNNs controller. Finally, several simulation results including two-order and three-order MIMO non-affine system in non-triangular form, double pendulums system, inverted double pendulums on cars system, two degree of freedom helicopter (2 DOF-Helicopter) system, and multi-link robot system are shown to demonstrate the performance of our approaches.

Abstract in Chinese i
Abstract in English iii
Acknowledgements in Chinese v
Contents vi
List of Figures viii
List of Tables xii

CHAPTER 1.　Introduction 1
CHAPTER 2.　Preliminaries 5
2.1　 Problem Formulation 5
2.2　 Output Recurrent Wavelet Neural Network (ORWNN) 9
2.2.1 Approximation Analysis 13
CHAPTER 3.　Improved Adaptive Backstepping Control Using ORWNNs 17
3.1　Introduction 17
3.2　Adaptive Backstepping Control for MIMO Nonlinear Non-affine Systems 18
3.2.1　ORWNN Estimator 18
3.2.2 Adaptive Backstepping Control Approach Using ORWNNs (ABC) 20
3.3 Improved Adaptive Backstepping Control Approach Using Dynamic Surface Control 32
3.4　Simulation Results and Comparisons 45
3.4.1 MIMO Nonlinear Non-affine System 45
Example 3.1 Two-order MIMO Non-affine System in Non- triangular Form 45
Example 3.2 Three-order MIMO Non-affine System in Non- triangular Form 54
Example 3.3 Tracking Control of a Non-affine Double-Pendulums System 60
3.4.2 MIMO Nonlinear Affine System 67
Example 3.4 Inverted Double Pendulums on Carts System 67
Example 3.5 Tracking Control of Quanser-DOF Helicopter System 73
Example 3.6 Tracking Control of Robot-Arm System 78
Two-link Robot System 78
3.5 Conclusions 82
CHAPTER 4. Direct Adaptive ORWNNs Control Via Backstepping Design Technique 83
4.1 Introduction 83
4.2 Direct Adaptive ORWNNs Backstepping Control Design 84
4.2.1 ORWNNs Controller 84
4.3 Simulation Results and Comparisons 93
4.3.1 MIMO Nonlinear Non-affine System 93
Example 4.1 Two-order MIMO Non-affine System in Non- triangular Form 93
Example 4.2 Three-order MIMO Non-affine System in Non- triangular Form 97
Example 4.3 Tracking Control of a Non-affine Double-Pendulums System 103
4.3.2 MIMO Nonlinear Affine System 106
Example 4.4 Inverted Double Pendulums on Carts System 106
Example 4.5 Tracking Control of Quanser-DOF Helicopter System 110
Example 4.6 Tracking Control of Two-link Robot System 114
4.4 Conclusions 116
CHAPTER 5.　Conclusions and Future Researches 117
APPENDIX Flowchart of Controller Design 119
REFERENCES 122

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