Robust State-Derivative Feedback Fuzzy Control with Stability and Passivity Constraints for Singular Perturbed Systems

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Project title

Code/計畫編號

MOST109-2221-E019-049

Translated Name/計畫中文名

滿足穩定和被動限制下針對奇異擾動系統探討強健狀態微分回授模糊控制之研究

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=13540633

Year

2020

Start date/計畫起

01-08-2020

Expected Completion/計畫迄

31-07-2021

Bugetid/研究經費

961千元

ResearchField/研究領域

電子電機工程

在本計畫中，我們將探討狀態微分回授模糊控制之研究，針對連續時間之非線性奇異擾動系統和非線性奇異隨機系統以確保其閉迴路系統之穩定性及性能需求。我們將利用Takagi-Sugeno (T-S) 模糊模型來表示非線性奇異擾動系統和奇異隨機系統。基於模糊控制理論、Lyapunov穩定理論、被動條件、狀態微分回授等方法，我們將透過Takagi-Sugeno模糊模型探討非線性奇異系統穩定性問題的分析及解析。根據非線性奇異擾動Takagi-Sugeno模糊模型和非線性奇異隨機Takagi-Sugeno模糊模型，本計畫將發展一個以平行分佈補償為基礎之模糊控制器設計方法來滿足閉迴路系統的穩定性。以Lyapunov穩定理論為基礎，我們在模糊控制器的設計程序中也考慮了衰退率的加入，再針對隨機行為也考慮被動限制來抑制系統中的隨機行為，用以改善非線性奇異系統的暫態響應。綜言之，本計畫之主要貢獻是希望將狀態微分回授方法使用在連續時間之非線性奇異系統上，試圖解決數學的困難以求得精簡的穩定條件，順利設計出具有良好暫態響應特性的模糊控制器。最後，我們將進行電腦數值模擬來驗證本計畫所提出的模糊控制方法之可行性及可應用性。In this proposal, we will study the state-derivative feedback fuzzy control to guarantee the closed-loop system stability and performance requirement for the continuous-time nonlinear singular perturbed systems and nonlinear singular stochastic systems. The Takagi-Sugeno (T-S) fuzzy model is applied to represent the nonlinear singular perturbed systems and nonlinear singular stochastic systems. Based on the fuzzy control theory, Lyapunov stability theory, passivity constraint, and state-derivative feedback method, we will discuss the stability analysis and synthesis of the nonlinear singular systems via Takagi-Sugeno fuzzy models. According to the nonlinear singular perturbed Takagi-Sugeno fuzzy models and nonlinear singular stochastic Takagi-Sugeno fuzzy models, a parallel distributed compensation based fuzzy controller design approach is developed in this proposal to achieve the closed-loop system stability. Based on the Lyapunov stability theory, the decay rate is also considered in the proposed fuzzy controller design process to improve the transient responses for the nonlinear singular systems. To deal with the stochastic of the systems, we choose the passivity constraint to inhibition the stochastic behavior of the singular system. These relaxed stability conditions can be easily solved by the well-known linear matrix inequality technique. The main contribution of this proposal is to overcome the mathematical problem to obtain compendious stability conditions and better transient responses when one uses the state-derivative feedback method to design a fuzzy controller for the continuous-time nonlinear singular systems. At last, some computer simulations are provided to show the feasibility and applicability of the proposed fuzzy control approach.

Keyword(s)

非線性奇異擾動系統
非線性奇異隨機系統
Takagi-Sugeno模楜模型
強健模糊控制
狀態微分回授
被動線制
Nonlinear Singular Perturbed Systems
Nonlinear Singular Stochastic Systems
Takagi-Sugeno Fuzzy Model
Robust Fuzzy Control
State-derivative Feedback
Passivity Constraint

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Robust State-Derivative Feedback Fuzzy Control with Stability and Passivity Constraints for Singular Perturbed Systems

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