Passive Fuzzy Controller and Observer Design for Nonlinear Stochastic Systems with Multiplicative Noises

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Project title

Code/計畫編號

NSC98-2221-E019-034

Translated Name/計畫中文名

具乘積雜訊非線性隨機系統之被動模糊控制器與模糊觀測器設計

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=1913375

Year

2009

Start date/計畫起

01-08-2009

Expected Completion/計畫迄

31-07-2010

Bugetid/研究經費

640千元

ResearchField/研究領域

電子電機工程

"近年來，學者們針對隨機系統的研究與討論投入了大量的努力與心血，其中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。對此系統，Itô 準則被發展來探討並進行穩定性分析之過程。 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。本計畫中，我們將利用Langevin 方程式架構出非線性隨機系統的隨機T-S 模糊模型。在模糊控制的程序中，我們亦將考慮時間延遲及系統內部擾動效應對隨機T-S 模糊模型之影響。為了探討雜訊對非線性隨機系統之影響，我們所考慮的隨機T-S 模糊模型也將加入外部雜訊的干擾。利用被動理論，本計畫將開發模糊控制器與觀測器以使非線性隨機系統達到消除外部雜訊干擾之性能。在本計畫中，我們提出了三年的研究計畫，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被動性之控制問題。在第一年計畫中，我們首先利用T-S 模糊模型考慮具乘積雜訊非線性隨機系統的穩定性分析與解析，為了更接近真實操作環境，我們對隨機系統加入了時間延遲的考量，並且針對具乘積雜訊之時間延遲非線性隨機系統發展出一套模糊控制器的設計流程。第二年，為了考慮建模誤差或內部元件擾動所造成的不明確性，我們將加入系統內部擾動特性的影響。在考慮這些系統內部擾動的影響下，我們將發展出具乘積雜訊非線性隨機系統之充分穩定條件，根據此穩定條件，我們便可設計模糊控制器來保證系統具備強健穩定與被動的特性。在第三年的計畫中，我們將針對具乘積雜訊非線性隨機系統探討以觀測器作為回授之模糊控制器設計。透過模糊觀測器的設計，在系統狀態無法完全量測的情況下，我們亦可以用觀測器作為回授信號，以完成利用狀態估測回授來設計穩定模糊控制器的目標。有關本計畫的內容，我們將以下表作為整合說明。"
"Recently, many researchers pay their attentions to study the control problem for the stochastic systems. 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. For stochastic systems with multiplicative noise terms, the Itô’s formula was developed for analyzing the stability of stochastic 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 controller. By using the T-S fuzzy control approach, the linear control theory can be used to analyze and synthesize the stability of nonlinear systems. The stochastic T-S fuzzy model structured by Langevin equation is proposed to represent the nonlinear stochastic systems in this proposal. During the fuzzy control process, the time delay and internal perturbation effects are also considered on the stochastic T-S fuzzy models. In order to discuss the disturbance effect on nonlinear stochastic systems, the stochastic T-S fuzzy model with external disturbance is considered. By applying the passivity theory, a fuzzy controller and observer will be developed in this proposal such that the nonlinear stochastic systems achieve the attenuation performance. In this proposal, we will carry on our research results for guaranteeing the stability and passivity of continuous and discrete nonlinear stochastic systems with multiplicative noises in three years. In the first year, we will discuss the stability analysis and synthesis of nonlinear stochastic systems with multiplicative noises via T-S fuzzy model. For approximating the real environment, the time-delay effects on systems are considered in this year. We will develop a fuzzy controller design process for time-delay nonlinear stochastic systems with multiplicative noises. In the second year, the uncertainties constructed from modeling errors or varying of elements will be considered. According to these internal perturbations, we will develop sufficient stability conditions for nonlinear stochastic systems with multiplicative noises. From the stability conditions, a fuzzy controller can be designed to guarantee the robust stability and passive properties of systems. In the third year, the observer-based fuzzy control for the nonlinear stochastic systems with multiplicative noises is studied. With fuzzy observer, the information of system states can be measured to realize the fuzzy controller with state feedback law when the state variables cannot be measured. The contents of this proposal can be collated as the following table."

Keyword(s)

模糊控制
Takagi-Sugeno 模糊模式
被動理論
隨機系統
線性矩陣不等式
Fuzzy Control
Takagi-Sugeno Fuzzy Models
Passivity Theory
Stochastic Systems
Linear Matrix Inequality

DSpace CRIS

Passive Fuzzy Controller and Observer Design for Nonlinear Stochastic Systems with Multiplicative Noises

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