Robust Fuzzy Controller Design for Nonlinear Perturbed Stochastic Systems Subject to State Variance and Passivity Constraints

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Project title

Code/計畫編號

NSC102-2221-E019-051

Translated Name/計畫中文名

非線性擾動隨機系統滿足狀態方差及被動限制之強健模糊控制器設計

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=3117380

Year

2013

Start date/計畫起

01-08-2013

Expected Completion/計畫迄

31-07-2014

Bugetid/研究經費

806千元

ResearchField/研究領域

電子電機工程

"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擾動隨機系統的個別狀態方差限制之控制器設計問題。 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。根據 T-S 模糊建模的技術，我們先前的國科會專題研究計畫 NSC101-2221-E-019-036 已針對非線性隨機系統探討滿足個別狀態方差限制的控制器設計問題。經由改良協方差控制理論，我們可運用 T-S 模糊模型針對非線性隨機系統發展模糊控制器的設計方法。延伸計畫 NSC101-2221-E-019-036 所得的結果，本計畫中我們期望針對具乘積雜訊之非線性擾動隨機系統，探討強健模糊控制器的設計問題。除了考慮系統的穩定性能外，本計畫亦同時考慮個別狀態方差限制及被動特性限制。我們將利用擾動隨機 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，以使具乘積雜訊之擾動隨機 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擾動隨機 T-S 模糊模型滿足系統穩定限制、個別狀態方差限制及被動特性限制等行為需求。"
"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 perturbed stochastic systems due to the complexity of mathematic computations. 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. Based on the T-S fuzzy modeling technique, our previous project NSC101-2221-E-019-036 dealt with 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 has been developed by modifying the covariance control approach. Extending the results of project NSC101-2221-E-019-036, we will carry on our research results for designing robust fuzzy controller of the nonlinear perturbed stochastic systems with multiplicative noises in this proposal. In addition to the stability performance, the individual state variance constraints and passivity constraints are also considered in this proposal. We will discuss the stability analysis and synthesis of nonlinear perturbed stochastic systems with multiplicative noises via perturbed stochastic T-S fuzzy models. A PDC-based fuzzy controller design process is developed for the perturbed 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 constraint, individual state variance constraint and passivity constraint for the continuous-time and discrete-time perturbed stochastic T-S fuzzy models with multiplicative noises."

Keyword(s)

非線性擾動隨機系統
模糊控制器設計
方差限制
被動特性限制
線性矩陣不等式
Nonlinear Perturbed Stochastic Systems
Fuzzy Controller Design
State Variance Constraint
Passivity Constraint and Linear Matrix Inequality

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Robust Fuzzy Controller Design for Nonlinear Perturbed Stochastic Systems Subject to State Variance and Passivity Constraints

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