基於模糊c-回歸模型分類與新穎群集驗證準則之模糊模型辨證及其應用

Fuzzy Model Identification by FCRM Clustering with Novel Cluster Validity Criteria and its Applications

蘇瑞堯(Jui-Yiao Su)

指導教授 ： 龔宗鈞

大同大學/電機資訊學院/電機工程學系所/博士(2007年)

摘要

本論文主要是針對非線性系統提出有效的方法與步驟以辨證其模糊模型。首先，吾人利用模糊c-回歸模型分類演算法(fuzzy c-regression model clustering)將系統的輸入-輸出資料進行『超平面』(hyper-plan-shaped)群集分類。每一群集本質上可視為一條描述系統輸入-輸出響應的模糊模型規則，而群集的數目即為模糊模型所需的模糊規則數目。本論文特別針對模糊c-回歸模型分類演算法提出四種新穎的群集驗證準則以供判定最適當的群集數目（模糊規則數目）。一旦群集數目決定了，吾人即可逐一建構其模糊模型規則。每一條模糊模型規則的後件部參數可以直接由模糊c-回歸模型分類演算法所產生的群集表示式（cluster representatives）所獲得（線性或仿射線性回歸函數）。而前件部模糊集合則利用投射法（projection method），將模糊分割矩陣U（fuzzy partitions matrix）投射在每個前件變數座標軸上先獲得點狀分佈的模糊集合(point-wise defined fuzzy set)，再以一般鐘型歸屬函數(bell-shaped membership function)近似之。此外，本論文亦提出一檢驗與重新分割法（check and repartition algorithm）以避免不同區域之資料共用同一回歸函數所衍生的不良前件部結構(inappropriate premise structure)。最後，吾人再以梯度陡降法(gradient descent algorithm)為所獲得的模糊模型進行細部調整，以期以系統化的步驟，用最精簡的模糊規則數目建構出最有效能的模糊模型。
在應用方面，本文亦針對未知之離散時間非線性系統（discrete-time nonlinear systems）提出兩種模糊模型控制器（fuzzy model based controllers: FMBC)之設計方法。首先，吾人應用前述之模糊模型辨證方法，以最精簡的模糊規則數目為其建構模糊模型，再基於該模糊模型來設計相對應的FMBC。第一種FMBC可令受控系統達成追蹤參考訊號之控制目標。第二種FMBC則進一步藉由解線性矩陣不等式(linear matrix inequalities :LMIs)的方法，令受控系統達成 追蹤之控制目標。
根據各項模擬結果顯示，本論文所提出的模糊模型辨證方法與模糊模型控制器十分準確且有效。

關鍵字

群集驗證準則 ； 模糊c-回歸模型分類演算法 ； 模糊模型辨證 ； 模糊模型控制器

並列摘要

In this thesis, an effective approach is developed to establish fuzzy models for a given nonlinear system. Firstly, the fuzzy c-regression model (FCRM) clustering technique is applied to partition the product space of the given input-output data into hyper-plan-shaped clusters. Each cluster is essentially a basis of the fuzzy rule that describes the system behavior, and the number of clusters is just the number of fuzzy rules. Particularly, several novel cluster validity criteria for FCRM clustering are set up to choose the appropriate number of clusters (rules). Once the number of clusters is determined, the consequent parameters of each IF-THEN rule are directly obtained from the functional cluster representatives (linear or affine linear regression models). The antecedent fuzzy sets of each IF-THEN fuzzy rule are acquired by projecting the fuzzy partitions matrix U onto the axes of individual antecedent variable to obtain point-wise defined fuzzy sets and to approximate these point-wise defined fuzzy sets by normal bell-shaped membership functions. Additionally, a check and repartition algorithm is suggested to prevent the inappropriate premise structure where separate regions of data shared the same regression model. Finally, the gradient descent algorithm is included to adjust the fuzzy model precisely. A fuzzy model with compact IF-THEN rules could thus be generated systematically.
Once a reasonably accurate fuzzy model of the consider process is available, it can be used as a part of the fuzzy model based control (FMBC) scheme. In this thesis, two FMBC are proposed for discrete-time nonlinear systems as well. The first FMBC is designed to make the plant track the reference trajectory signal with stable error dynamic. The second FMBC can stabilize the NARMA (nonlinear auto-regressive moving average) system with tracking performance by solving the linear matrix inequalities (LMIs).
Several simulation examples are provided to demonstrate the accuracy and effectiveness of the fuzzy modeling algorithm and the controllers.

並列關鍵字

cluster validity criteria ； fuzzy c-regression model (FCRM) clustering ； fuzzy model identification ； fuzzy model based control

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