Sliding Mode Fuzzy Control with Variance and Passivity Constraints for Nonlinear Stochastic Systems

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Project title

Code/計畫編號

MOST103-2221-E019-043

Translated Name/計畫中文名

方差與被動限制下之非線性隨機系統的滑動模式模糊控制研究

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=8352025

Year

2014

Start date/計畫起

01-08-2014

Expected Completion/計畫迄

31-07-2015

Bugetid/研究經費

660千元

ResearchField/研究領域

電子電機工程

"本計畫應用滑動模式控制的技術處理非線性隨機系統控制問題，此外，也探討了滿足個別狀態方差限制及被動限制之控制問題。透過Takagi-Sugeno (T-S) 模糊模型和 Langevin 線性方程式，提供一個有效且有用的方法來近似非線性隨機系統，以隨機T-S模糊模型為基礎進行滑動模式模糊控制，且同時考慮個別狀態方差限制及被動限制的行為需求，此外，我們也透過平行分佈補償 (PDC) 的觀念設計針對非線性隨機系統設計穩定的模糊控制器。對隨機系統而言，通常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。此外，在文獻中，被動限制常被用來探討系統受雜訊的影響，進而希望達到消弭雜訊的目的。因此，本計畫之動機在於嘗試同時發展滿足非線性隨機系統個別狀態方差限制及被動限制之滑動模式模糊控制器的設計方法。利用隨機 T-S 模糊模型來表示非線性隨機系統的應用下，發展了一個結合滑動模式控制理論、協方差控制理論被動控制理論的改良型控制器設計方法。在本計畫中，我們分別針對連續型與離散型非線性隨機系統，探討滿足閉迴路系統穩定性、個別狀態方差限制與被動限制之控制問題。我們將利用隨機T-S模糊模型來探討非線性隨機系統的穩定性分析與解析。再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為基礎的滑動模式模糊控制器設計方法在本計畫中被開發，本計畫之方法所設計的滑動模式模糊控制器使隨機 T-S 模糊模型滿足閉迴路系統穩定性、個別狀態方差限制與被動限制的行為需求。最後藉由模擬結果發現我們所研發的方法具有較好的追蹤響應能力、抵抗系統不確定誤差能力、雜訊消弭之能力，同時並能滿足個別狀態方差限制之需求。"
"This project applies the sliding mode control technique to solve the control problems of nonlinear stochastic systems. And, the system achieves individual state variance constraint and passivity constraint. It is well known that T-S fuzzy model and Langevin linear function provide an effective and useful technique to approximate nonlinear stochastic systems. Based on the T-S fuzzy stochastic model, the technique of Parallel Distribution Compensated (PDC) can be employed to design stable fuzzy controllers for nonlinear stochastic 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. Besides, in literature, the passivity constraint is employed to discuss the effect of disturbance on system such that the attenuation performance is achieved. Therefore, this project proposes the sliding model fuzzy controllers design methods for the nonlinear stochastic systems methods and satisfy the individual state variance constraint and passivity constraint. In this project, we will carry on our research results for guaranteeing the closed-loop system stability, individual state variance constraint and passivity constraint of continuous-time and discrete-time nonlinear stochastic systems. We will discuss the stability analysis and synthesis of nonlinear stochastic systems via stochastic T-S fuzzy models. Employing the Linear Matrix Inequality (LMI) technique to solve the Lyapunov stability conditions, a PDC-based sliding mode fuzzy controller design approach is proposed in this project to achieve the closed-loop system stability, individual state variance constraint and passivity constraint for stochastic T-S fuzzy models. Finally, via the simulation results, our methods have the ability of good tracking response, uncertain plant error term rejection, noise attenuation and satisfying individual state variance constraint."

Keyword(s)

非線性隨機系統
模糊控制
協方差控制
滑動模式控制
方差限制
被動限制
Nonlinear Stochastic Systems
Fuzzy Control
Covariance Control
Slide Mode Control
Variance Constraint and Passivity Constraint

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Sliding Mode Fuzzy Control with Variance and Passivity Constraints for Nonlinear Stochastic Systems

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