本文提出一個具非對稱歸屬函數(或可稱為Footprint Of Uncetainty, FOU)之第二型模糊類神經網路，並應用至非線性系統鑑別與控制。根據過去文獻提出的網路架構，本文以非對稱FOU取代常用的高斯對稱FOU。有別於高斯對稱FOU，非對稱FOU由四個高斯函數建構，可描述歸屬函數中心不明確(uncertain mean)與寬度不明確(uncertain variance)之特性，藉由非對稱之參數更新法則，可增加參數調整的效率與網路的近似能力。由系統鑑別的模擬結果可知，給定同樣的誤差需求，具非對稱FOU網路所使用的規則數與調整參數個數，皆少於對稱FOU網路。在非線性系統控制的應用上，對於可控典型式之受控系統，採用補償控制架構，配合Lyapunov穩定定理設計參數更新法則，模擬結果再次驗證使用非對稱FOU之優點；而對於非線性串接系統(nonlinear cascade system)，以backstepping之概念將系統視為兩個子系統，依序設計虛擬控制器(virtual controller)與實際控制器使原系統穩定，稱為解耦合控制架構，由非線性TORA系統與球桿系統模擬結果可證明其可行性與性能。

This thesis proposes a type-2 fuzzy neural network (type-2 FNN) with asymmetric membership functions (also called Footprint Of Uncertainty, FOU), and applies it to identification and control of nonlinear systems. Based on the previous type-2 FNN structure, the mostly used Gaussian symmetric FOUs are replaced by asymmetric ones. An asymmetric FOU consists of four Gaussian functions. It describes the properties of both uncertain mean (center) and uncertain variance (width) in membership functions. Based on the Lyapunov approach, the corresponding adaption laws are derived to increase the efficiency of tuning parameters, and the approximation ability. The type-2 FNN with asymmetric FOU has small network structure (fewer rules and tuning parameters than the one with symmetric FOU) from the simulation results of system identification. For nonlinear system control, a type-2 FNN controller and compensated control scheme are used to treat the control problem of system with controllable canonical form. Based on the Lyapunov approach, the adaption laws and stability are also guaranteed. By the concept of backstepping, a nonlinear cascade system is decoupled into two sub-systems, then virtual controller and actual controller are designed sequentially to stabilize the system. Simulation results demonstrate the performance of our approach.

中文摘要.....i
英文摘要.....ii
誌 謝.....iii
目 錄.....iv
圖 目 錄.....vi
表 目 錄.....ix

第一章、前言.....1
1.1 文獻回顧.....1
1.2 研究動機與目的.....3
第二章、模糊邏輯系統(Fuzzy Logic System, FLS).....5
2.1 第一型模糊邏輯系統(Type-1 FLS).....5
2.2 第二型模糊邏輯系統(Type-2 FLS).....6
2.3 區間第二型模糊邏輯系統(Interval Type-2 FLS).....8
2.3.1 區間第二型歸屬函數(Interval Type-2 MFs).....9
2.3.2 區間第二型模糊推論(Interval Type-2 Fuzzy Inference).....11
2.3.3 區間第二型模糊集合之重心(Centroid of an Interval Type-2 Fuzzy Set)....15
2.3.4 降階運算(Type-Reduction)與解模糊(Defuzzification).....17
第三章、非對稱FOU之第二型模糊類神經網路(Type-2 Fuzzy Neural Network with Asymmetric FOU).....21
3.1 非對稱FOU (Asymmetric FOU).....21
3.2 網路架構.....25
3.3 倒傳遞學習演算法(Back-Propagation Learning Algorithm, BP).....31
3.4 穩定性分析.....37
第四章、非線性系統鑑別與時間序列預測.....41
4.1 非線性系統鑑別.....41
4.1.1 例4.1.....42
4.1.2 例4.2.....47
4.2 Mackey-Glass時間序列預測.....52
第五章、非線性系統控制.....62
5.1 可控典型式系統之補償控制架構.....62
5.2 倒單擺系統穩定與追蹤控制.....70
5.3 非線性串接系統之解耦合控制架構.....78
5.4 球桿系統之穩定與追蹤控制.....82
5.5 TORA系統之穩定與追蹤控制.....88
第六章、結論.....95
附錄一、BP參數更新法則推導.....97
附錄二、補償控制穩定性推導.....108
參考文獻.....111

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