為了在非線性不確定系統下解決多目標H2/H infinity模糊追蹤控制問題，本篇論文中提出一個多目標模糊控制設計使在非線性不確定系統下能夠保證H2和H infinity的軌跡追蹤效能可以同時滿足。首先利用T-S fuzzy model來使線性系統近似非線性不確定系統，接著基於T-S fuzzy model和模糊控制器所組成的擴充矩陣，多目標H2/H infinity模糊追蹤控制問題可以被公式化成一個多目標問題來同時最小化非線性模糊問題的H2追蹤誤差和H infinity擾動抑制程度。因為直接解多目標問題不容易，所以提出一個間接的方法來解決多目標控制設計問題，即假設H2追蹤誤差和H infinity擾動抑制程度有其上界，然後藉由盡量降低這兩個上界達到同時最小化H2和H infinity，讓多目標問題轉變成最小化帶有三個線性矩陣不等式限制條件的多目標控制設計問題。接著藉由MATLAB的LMI toolbox使用結合了線性矩陣不等式的多目標演化演算法從多目標問題得出的一組Pareto最佳化解讓使用者可以根據使用需要來挑選。另外，為了與本篇論文提出的多目標控制設計方法做比較，也展示用weighted sum 方法解決多目標H2/H infinity模糊追蹤控制設計問題，同時在本篇論文中也簡述了演化演算法的設計流程。最後，給出一個二連桿機器手臂的例子來說明設計流程及證明帶有線性矩陣不等式約束的多目標演化演算法在非線性不確定系統下對H2/H infinity模糊追蹤控制問題的表現。

In this study,in order to solve multiobjective H2/H infinity fuzzy tracking control problem in nonlinear uncertain system, a multiobjective fuzzy control design method is introduced for nonlinear uncertain systems to guarantee optimal H2 and H infinity reference tracking performance simultaneously. First, the Takagi and Sugeno (T-S) fuzzy model is used to represent the nonlinear uncertain system. Then, based on T-S fuzzy model and fuzzy controller, multiobjective H2/H infinity fuzzy tracking control problem is formulated as a multiobjective problem (MOP) to minimize the H2 tracking error and H infinity disturbance attenuation level for nonlinear fuzzy systems at the same time. Since it is not easy to solve this MOP directly, an indirect method is proposed to solve this MOP for multiobjective H2/H infinity fuzzy tracking control design, which is assuming that H2 tracking error and H infinity disturbance attenuation level have the upper bounds, and based on minimizing two upper bounds, the multiobjective problem is transformed to minimizing the multiobjective control design problem under the constraint of three linear matrix inequalities (LMIs). Then, a LMI-based multiobjective evolution algorithm (LMI-based MOEA) which used the LMI toolbox in MATLAB is developed to efficiently solve the set of Pareto optimal solutions for the MOP, from which designer can select one design according to his own preference. Further, the multiobjective H2/H infinity fuzzy control design problem based on the weighted sum method is also solved for comparison, and we also introduce the evolution algorithm in this paper.Finally, a numerical simulation is given to illustrate the design procedure and to confirm the performance of the proposed multiobjective H2/H infinity fuzzy tracking control for nonlinear uncertain system.

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