Individual State Variance Constrained Fuzzy Controller Design for Nonlinear Multiplicative Noised Stochastic Systems

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Project title

Code/計畫編號

NSC101-2221-E019-036

Translated Name/計畫中文名

滿足非線性乘積雜訊隨機系統個別狀態方差限制之模糊控制器設計

Project Coordinator/計畫主持人

Wen-Jer Chang

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Marine Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=2642646

Year

2012

Start date/計畫起

01-08-2012

Expected Completion/計畫迄

31-07-2013

Bugetid/研究經費

706千元

ResearchField/研究領域

電子電機工程
數學

"近年來，隨機動態系統的穩定性與穩定化問題格外受到學者們的重視，這些隨機動態系統常以Langevin 形式的隨機微分方程式及差分方程式來表示。在隨機系統的模組化技術中，Langevin 方程式被廣泛的應用於描述隨機系統，該方程式透過狀態與雜訊相乘的項次來描述隨機系統中之隨機行為，因此，其非線性隨機系統具有雙線性系統之特性。 Takagi-Sugeno (T-S) 模糊模型提供了一個有效且有用的方法來近似非線性系統。以T-S 模糊模型為基礎，我們可透過平行分佈補償 (PDC) 的觀念設計穩定的模糊控制器。利用T-S 模糊控制方法，我們可以使用線性控制理論來針對非線性系統進行穩定性分析與控制器的設計。對隨機系統而言，透過最小化一個數值加權成本函數，線性二次高斯 (LQG) 最佳控制方法經常被用來探討狀態方差限制的問題。但不幸地，最佳控制理論無法確保系統個別狀態方差限制的行為需求被滿足。為了解決這個問題，協方差控制理論已被成功地應用在線性及雙線性隨機系統，以求得滿足個別方差限制的控制器。然而，由於數學運算的複雜性，幾乎很少看到學者們探討非線性隨機系統的個別狀態方差限制之控制器設計問題。因此，本計畫之動機在於嘗試發展滿足非線性隨機系統個別狀態方差限制之控制器的設計方法。在利用 T-S 模糊模型來表示非線性隨機系統的應用下，本計畫將發展一個結合改良型協方差控制理論的模糊控制器設計方法。在本計畫中，我們期望針對具乘積雜訊之連續型與離散型非線性隨機系統，探討滿足系統穩定性與個別狀態方差限制之控制問題。我們將利用隨機T-S 模糊模型來探討具乘積雜訊非線性隨機系統的穩定性分析與解析，我們亦將發展一個以平行分佈補償觀念為基礎的模糊控制器設計程序，以使具乘積雜訊之隨機T-S 模糊模型達到穩定。在利用線性矩陣不等式 (LMI) 的技術求解里亞普諾夫 (Lyapunov) 穩定條件的應用下，一個以平行分佈補償觀念為基礎的模糊控制器設計方法將在本計畫中被開發，本計畫之方法所設計的模糊控制器將使具乘積雜訊之連續型與離散型隨機 T-S 模糊模型滿足系統個別狀態方差限制的行為需求。"
"Recently, the stability and stabilization problems of stochastic dynamic systems have attracted much attention via stochastic differential and difference equations which are described by Langevin form. In stochastic modeling techniques, the Langevin equation is widely applied for describing the behaviors of stochastic systems. The Langevin equation uses the multiplicative noise terms to structure the stochastic systems; hence, the stochastic systems can be considered as bilinear systems. The Takagi-Sugeno (T-S) fuzzy model provides an effective and useful technique to approximate nonlineaties of nonlinear systems. Based on the T-S fuzzy model, the concept of Parallel Distribution Compensated (PDC) technique can be employed to design stable fuzzy controllers. By using the T-S fuzzy control approach, the linear control theory can be used to analyze and synthesize the stability of nonlinear systems. For stochastic systems, the Linear Quadratic Gaussian (LQG) optimal control approach is usually used to study the state variance constrained problem via minimizing a weighted cost function. Unfortunately, the optimal control theory does not ensure that the individual state variance constraints are satisfied. In order to solve this problem, the covariance control theory has been successfully employed to design variance constrained controllers for linear and bilinear stochastic systems. However, there are few researchers discuss this control problem for the nonlinear stochastic systems due to the complexity of mathematic computations. Therefore, the motivation of this proposal is to study the individual state variance constrained controller design problem for the nonlinear stochastic systems. By using T-S fuzzy models to represent the nonlinear stochastic systems, a fuzzy controller design methodology is developed in this proposal by modifying the covariance control approach. In this proposal, we will carry on our research results for guaranteeing the stability and individual state variance constraints of continuous-time and discrete-time nonlinear stochastic systems with multiplicative noises. We will discuss the stability analysis and synthesis of nonlinear stochastic systems with multiplicative noises via stochastic T-S fuzzy models. A PDC-based fuzzy controller design process is developed for the stochastic T-S fuzzy models with multiplicative noises. Employing the Linear Matrix Inequality (LMI) technique to solve the Lyapunov stability conditions, a PDC-based fuzzy controller design approach is developed in this proposal to achieve the stability and individual state variance performance constraints for the continuous-time and discrete-time stochastic T-S fuzzy models with multiplicative noises."

Keyword(s)

隨機Takagi-Sugeno 模糊模型
模糊控制理論
協方差控制理論
線性矩陣不等式
Stochastic Takagi-Sugeno Fuzzy Models
Fuzzy Control Theory
Covariance Control Theory and Linear Matrix Inequality

DSpace CRIS

Individual State Variance Constrained Fuzzy Controller Design for Nonlinear Multiplicative Noised Stochastic Systems

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