線性矩陣不等式的強健適應滑差控制應用於T-S模糊系統

Abstract

物理系統自然形成非線性，因此，所有的控制系統都是具有某些程度的非線性。過去超過二十年時間，模糊技術已經廣泛地成功被利用在非線性系統模型建立與控制器設計。近十年來，T-S模糊模型在處理複雜的非線性系統是一個廣為流傳且使用方便的工具。同樣地，對於非線性系統的模糊迴授控制設計問題已經廣泛地被研究藉由使用T-S模型，其中用簡單的局部線性模型被組合去描述非線性系統的全域行為。實際上，不可避免的不確定性也許會以一種非常複雜的方式進入到一個非線性系統模型。此不確定性也許包含模型誤差、參數變化、外部干擾和模糊近似誤差。在如此的一個情況下，模糊迴授控制設計方法也許不再運作良好。 在本論文中，我們首先提出強健適應滑差控制（包含滑差控制和適應控制）應用於具有範數界限外部干擾的T-S模糊模式，同時放寬每一個正規的局部系統模式擁有相同輸入通道的限制假設，這個限制假設是傳統可變結構模糊控制設計方法所需要的。然後，提出具有非相配參數變動和外部擾動的T-S模糊模式之強健適應滑差控制。此外，針對具有非相配參數變動和外部擾動的T-S模糊時間延遲模式，其強健適應滑差控制亦被提出。最後，利用一些例子來驗證本論文所提出方法的有效性和可行性。

Physical systems are inherently nonlinear. Thus, all control systems are nonlinear to a certain extent. Over the past two decades, fuzzy techniques have been widely and successfully exploited in nonlinear system modeling and control. In last ten years, the Takagi-Sugeno (T-S) fuzzy model is a popular and convenient tool for handling complex nonlinear systems. Correspondingly, the fuzzy feedback control design problem for a nonlinear system has been studied extensively by using the T-S model where simple local linear models are combined to describe the global behavior of the nonlinear system. In practice, the inevitable uncertainties may enter a nonlinear system model in a very complicated way. The uncertainty may include modeling errors, parameter variations, external disturbances, and fuzzy approximation errors. In such a situation, the fuzzy feedback control design methods may not work well anymore. In this dissertation, firstly, we propose two kinds of LMI-based robust adaptive sliding control, including a robust sliding control method and a robust adaptive control method, for uncertain Takagi-Sugeno fuzzy models with norm-bounded uncertainties, and meantime relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS-based fuzzy control design methods. Then, two kinds of LMI-based robust adaptive sliding control are developed for uncertain T-S fuzzy models which include mismatched parameter uncertainties and external disturbances. Moreover, two kinds of LMI-based robust adaptive sliding control are proposed for the uncertain T-S fuzzy time-delay model which includes mismatched parameter uncertainties in the state matrix and norm-bounded external disturbances. Finally, some examples are used to illustrate the effectiveness and usefulness of the proposed methods in this dissertation.