臺灣博碩士論文加值系統

本論文首先提出一種新的正交函數計算法來求解Takagi-Sugeno (TS) 模糊模型動態時延方程式。所提出的新方法，不需經由複雜的微分與積分計算，僅包含矩陣代數的運算，因此有助於電腦的運算過程可簡易並快速地完成，同時也可降低運算的複雜度。然後，舉一數值例來驗證所提出之正交函數計算法的有效性。接下來，使用正交函數計算法將TS模糊模型動態時延控制系統的穩定二次有限時間最佳平行分配補償控制的設計問題，轉換成由代數方程式型態來表示的靜態最佳化問題，而在論文中之二次有限時間積分的性能指標，同樣也以正交函數計算法轉換成矩陣代數的型式，如此可簡化設計的複雜度，也有助於後續田口基因演算法的應用，並配合由線性矩陣不等式技巧所推導出的時延依賴穩定充分條件，共同來解決TS模糊模型動態時延控制系統的穩定二次有限時間最佳平行分配補償控制器的設計問題。文中也將針對上述的穩定二次有限時間最佳平行分配補償控制器的設計問題，舉出實例模擬說明，所提出之新設計方法的應用可行性。最後，針對時變TS模糊模型動態時延控制系統之穩定二次有限時間最佳模糊平行分配補償控制器設計問題，應用凸集合的概念與線性矩陣不等式技巧，推導出時延依賴穩定充分條件，再與正交函數計算法和田口基因演算法結合，在二次有限時間積分性能指標最小化的控制目標下，設計時變TS模糊模型動態時延控制系統的穩定二次最佳模糊平行分配補償控制器，並舉一設計例，來驗證本文所提出之設計方法的應用情形。

In this dissertation, the orthogonal-functions approach (OFA) is first proposed to solve the Takagi-Sugeno (TS) fuzzy-model-based time-delay dynamic equations. The new method simplifies the procedure of solving the TS-fuzzy-model-based time-delay dynamic equations (TSFMTDE) into the successive solution of a system of recursive formulae only involving the matrix algebra. The new proposed approach is non-iterative, non-differential, non-integral, straightforward, and well-adapted to the computer implementation. The computational complexity can therefore be reduced remarkably. An illustrated numerical example is given in order to demonstrate the availability of the presently proposed method. Next, for the finite-horizon optimal control problem of the TS-fuzzy-model-based time-delay control systems, by integrating the delay-dependent stabilizability condition, the OFA, and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented to design the stable and quadratic-optimal parallel-distributed-compensation (PDC) controllers. In this dissertation, the delay-dependent stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). The control objective of quadratic optimal fuzzy PDC controllers is to minimize a quadratic integral performance index, where the quadratic integral performance index is also converted into the algebraic form by using the OFA. Based on the OFA, the stable and quadratic-optimal PDC control problem for the TS-fuzzy-model-based time-delay control systems is replaced by a static parameter optimization problem represented by the algebraic equations with constraint of LMI-based stabilizability condition; thus greatly simplifying the stable and optimal PDC control design problem. The computational complexity for both differential and integral in the stable and optimal PDC control design of the original dynamic systems may therefore be reduced considerably. Then, for the static constrained-optimization problem, the HTGA is employed to find the stable and quadratic-optimal PDC controllers of the TS-fuzzy-model-based time-delay control systems. A design example of the stable and quadratic-optimal PDC controllers is given to demonstrate the applicability of the proposed approach. Finally, for the finite-horizon optimal control problem of a class of time-varying TS-fuzzy-model-based time-delay control systems, by complementarily fusing the OFA, the HTGA and the delay-dependent stabilizability condition, an integrative method is presented to design the stable and quadratic-optimal PDC controllers, where the delay-dependent stabilizability condition can be derived from the concept of convex sets and the LMI technique. A design example of the stable and quadratic-optimal PDC controllers of a class of the time-varying TS-fuzzy-model-based time-delay control systems is given to demonstrate the applicability of the proposed new integrative approach.

摘要
Abstract
誌謝
Contents
List of Tables
List of Figures
Chapter 1 Introduction
1.1 Background and Motivation
1.2 Organization of the Dissertation
Chapter 2 Analysis of TS-Fuzzy-Model-Based Time-Delay Control Systems via Orthogonal-Functions Approach
2.1 Solutions of Time-Varying TS-Fuzzy-Model-Based Time-Delay Dynamic Equations
2.2 Illustrative Example
2.3 Summary
Chapter 3 Stable and Quadratic-Optimal Control for the TS-Fuzzy-Model-Based Time-Delay Control Systems
3.1 Problem Statement
3.2 Stable and Quadratic-Optimal PDC Controllers Design
3.3 Illustrative Example
3.4 Summary
Chapter 4 Optimal and Stable PDC Controllers Design for a Class of Time- Varying TS-Fuzzy-Model-Based Time-Delay Systems
4.1 Problem Statement
4.2 Stable and Quadratic Finite-Horizon Optimal PDC Controllers Design
4.3 Illustrative Example
4.4 Summary
Chapter 5 Conclusions
Appendix A: Proof of Theorem in Chapter 3
Appendix B: Proof of Theorem in Chapter 4
References
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