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研究生:林俊民
研究生(外文):LIN, CHUAN-MIN
論文名稱:適應性模糊自組織遞迴小腦模型控制器於混沌系統同步控制之研究
論文名稱(外文):Study on Control of Chaotic Systems Using Adaptive Fuzzy Self-organizing Recurrent Cerebellar Model Articulation Controller
指導教授:王順源王順源引用關係
指導教授(外文):WANG, SHUN-YUAN
口試委員:王順源李清吟王順忠宋文財劉逢源
口試委員(外文):WANG, SHUN-YUANLEE, CHING-YINWANG, SHUN-CHUNGSUNG, WEN-TSAILIU, FOUN-YUAN
口試日期:2021-07-30
學位類別:博士
校院名稱:國立臺北科技大學
系所名稱:電機工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2021
畢業學年度:109
語文別:英文
論文頁數:94
中文關鍵詞:混沌系統奇異子分岔同步化小腦模型控制器自組織遞迴TSK模糊系統
外文關鍵詞:Chaotic SystemsAttractorSynchronizationCerebellar Model Articulation ControllerSelf-organizingTSK Fuzzy SystemsBifurcationRecurren
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混沌的特性使非線性週期系統具有短期可預測且可控制的性質。近年來混沌系統的控制一直在演進,其中混沌同步是研發系統控制器的重要過程。為讓混沌系統同步控制器進行非線性動態學習,本研究以小腦模型控制器(cerebellar model articulation controller, CMAC)來實現自組織混沌控制。為使非線性系統控制平滑穩定、提高計算精準度與學習速度,本文將Takagi–Sugeno–Kang (TSK)模糊規則與高斯函數納入控制器設定。有別於傳統模糊規則,TSK模糊系統是利用多模型(multimodel)方法來描述整體系統的行為,因此對系統行為有較高的解釋性。本研究提出的適應性TSK模糊自組織遞迴小腦模型控制器(adaptive Takagi-Sugeno-Kang fuzzy self-organizing recurrent cerebellar model articulation controller, ATFSORC)架構為一組TSK模糊自組織遞迴CMAC和TSK補償控制器。為降低ATFSORC結構複雜度,本研究使用符號距離測量主從系統的誤差,並以Lyapunov理論測試混沌同步系統的穩定性。相較於過往研究相聯記憶體為固定的層數,ATFSORC架構內的層數決策機制能夠依據主從系統的誤差數值進行動態調整。本研究設計的TSK補償器能夠使混沌系統同步速度增快。模擬結果指出,不同初始參數下,ATFSORC相較於過往CMAC與FCMAC混沌系統同步時,在控制性能、穩定性、追蹤誤差函數與收斂速度方面均有明顯的進步。

Chaotic characteristics provide nonlinear periodic systems with short-term predictable and controllable properties. Chaotic systems have continued to evolve, with chaotic synchronization being a critical process in developing system controllers. To synchronize a chaotic system with a controller and perform nonlinear dynamic learning, in this study, a cerebellar model articulation controller (CMAC) was used to conduct self-organizing chaotic control. To ensure the smoothness and stability of the nonlinear system and improve its computational precision and learning speed, Takagi–Sugeno–Kang (TSK) fuzzy rules and Gaussian functions were incorporated into the controller settings. Unlike conventional fuzzy rules, TSK fuzzy systems use multimodel descriptions of the behaviors of the entire system and can therefore more effectively explain system behaviors. The adaptive TSK fuzzy self-organizing recurrent cerebellar model articulation controller (ATFSORC) architecture proposed in this study is a set comprising a TSK fuzzy self-organizing recurrent CMAC and a TSK compensating controller. To reduce the structural complexity of the ATFSORC, errors from the master-slave system were measured using the signed distance function, and the stability of the chaotic synchronization system was tested using the Lyapunov function. Compared with reported mechanisms in which associative memory had a fixed number of layers, the mechanism for deciding the number of layers in an ATFSORC architecture can be dynamically adjusted according to the error value of the master-slave system. The TSK compensator designed in this study can accelerate the synchronization of chaotic systems. According to the simulation results, under different initial parameters, the ATFSORC demonstrated significant improvements in control performance, stability, tracking error function, and convergence speed during the synchronization of chaotic systems when compared with CMAC and fuzzy CMAC.

摘 要 ......................................................................................................................................... i
ABSTRACT .............................................................................................................................. iii
誌 謝 ........................................................................................................................................ v
Table of Contents ...................................................................................................................... vi
List of tables ............................................................................................................................ viii
List of figures ............................................................................................................................ ix
Chapter 1 Introduction ............................................................................................................ 1
1.1 Research motivation ...................................................................................................... 1
1.2 Research goals ............................................................................................................... 3
1.3 Literature review ........................................................................................................... 4
1.4 Outline ........................................................................................................................... 6
Chapter 2 Chaotic systems ...................................................................................................... 8
2.1 History of chaos ............................................................................................................ 8
2.2 Chaotic systems ........................................................................................................... 10
2.3 Principles of chaos ...................................................................................................... 11
2.3.1 Attractor ............................................................................................................ 13
2.3.2 Strange attractor ................................................................................................ 15
2.3.3 Bifurcation ........................................................................................................ 16
2.4 Chapter conclusion ...................................................................................................... 17
Chapter 3 CMACs ................................................................................................................. 18
3.1 Introduction ................................................................................................................. 18
3.2 CMAC structure .......................................................................................................... 20
3.3 CMAC working principles .......................................................................................... 21
3.3.1 Steps for parameter processing ......................................................................... 22
3.3.2 CMAC learning methods .................................................................................. 27
3.4 Chapter conclusion ...................................................................................................... 28
Chapter 4 ATFSORC in chaotic systems ...................................................................... 29
4.1 Introduction ................................................................................................................. 29
4.2 FCMACs ..................................................................................................................... 30
4.3 TSK fuzzy systems ...................................................................................................... 31
4.4 TFSORC architecture .................................................................................................. 33
4.5 Synchronous control of chaotic systems ..................................................................... 35
4.5.1 Dynamic behaviors of FitzHugh–Nagumo neurons .......................................... 38
4.5.2 Deriving stability ............................................................................................... 39
4.5.3 TSK compensating controller ........................................................................... 47
4.5.4 Simulation results and analysis of chaotic synchronized control...................... 51
4.6 Chapter conclusion ...................................................................................................... 78
Chapter 5 Conclusion and future research directions ................................................... 79
5.1 Conclusion ................................................................................................................ 79
5.2 Contributions ............................................................................................................ 79
5.3 Future research directions ........................................................................................ 80
References ................................................................................................................................ 82
Appendix .................................................................................................................................. 85
Symbols .................................................................................................................................... 89
作者簡介 .................................................................................................................................. 93
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