基於不確定性模糊類神經系統之建構與應用

Uncertain Rule-based Fuzzy Neural Systems Development and Applications

李易翰(Yi-Han Lee)

指導教授 ： 林志民

元智大學/電機通訊學院/電機工程學系/碩士(2012年)

https://doi.org/10.6838/YZU.2012.00308

摘要

本論文使用弦波函數之擾動提出基於不確定性模糊類神經系統 (uncertain rule-based fuzzy neural system using sinusoidal perturbation, UFNS-S)並應用於非線性系統之鑑別及控制。我們利用模糊類神經網路及弦波函數之擾動簡化區間型第二型模糊類神經網路之計算，由於基於不確定性模糊類神經網路的前件部及後件部皆含有弦波函數之擾動，將之取代區間型第二型模糊類神經網路中不確定性之足跡(Footprint of uncertainty)，如此UFNS-S可降低系統計算的複雜度及具有掌握系統不確定性之能力。此外，我們利用倒傳遞演算法來訓練UFNS-S之參數，並基於理亞普諾夫穩定分析，藉由選擇適當的學習率以確保UFNS-S之收斂能力。最後，利用幾個例子證明我們所提出之方法的效能，其中包含：計算複雜度之分析、非線性系統之鑑別以及雙軸機械手臂之追蹤控制。

關鍵字

模糊類神經系統 ； 不確定性 ； 李亞普諾夫定理 ； 非線性系統鑑別 ； 非線性系統控制

並列摘要

This paper proposes an uncertain rule-based fuzzy neural system using sinusoidal perturbation (UFNS-S) for identifying and controlling nonlinear system. The UFNS-S is proposed for simplifying the computational complexity of interval type-2 fuzzy neural network (IT2FNN) or interval type-2 fuzzy logic systems. The sinusoidal perturbations are adopted to combine with the fuzzy sets of antecedent and consequent part for UFNS-S, it is utilized to represent the footprint of uncertainty for interval type-2 fuzzy systems. Thus, the proposed UFNS-Ss reduce the computational complexity and have the ability of handling uncertainty. In addition, the back-propagation (BP) algorithm is adopted for training parameters of UFNS-S and to minimize the different between desired and UFNS-S’s outputs. Based on Lyapunov stability approach, the convergence of UFNS-S is guaranteed by choosing appropriate learning rates. In addition, the time-varying optimal learning rates are also derived to obtain the faster convergent speed. Finally, the effectiveness of the proposed approach is demonstrated by several examples that consist of computational complexity analysis, nonlinear system identification, and tracking control of two-link robot manipulator system.

並列關鍵字

nonlinear control ； fuzzy neural system ； uncertainty ； Lyapunov theorem ； nonlinear system identification

參考文獻

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[15] C. H. Lee and F. Y. Chang, “Interval Type-2 Recurrent Fuzzy Neural System for Nonlinear Systems Control Using Stable Simultaneous Perturbation Stochastic Approximation Algorithm,” Mathematical Problems in Engineering, Vol.2011, No. 102439, 21 pages, 2011.

[23] C. H. Lee and Y. C. Lin, “Robust Adaptive Control for Nonlinear Uncertain Systems Using Type-2 Fuzzy Neural Network System,” Mathematical Problems in Engineering, Vol. 2011, No. 604391, 25 pages, 2011.

[45] 胡子偉，結合區間第二型模糊非對稱歸屬函數及遞迴類神經網路系統之研究與應用，元智大學電機工程學系，碩士論文，2008。

[47] 張奉宇，新穎區間第二型模糊類神經系統之設計與應用，元智大學電機工程學系，碩士論文，2011。