到目前為止，具有跳躍擴散雜訊的非線性動力系統的非線性隨機L_∞-gain控制問題還沒有被傳統的控制方法所解決。本文提出了一種L_∞-gain方法來處理非線性隨機控制問題。首先採用Takagi-Sugeno（T-S）模糊模型對非線性動力系統進行線性近似。接下來，基於T-S模糊模型，設計了一種基於模糊觀測器的控制器，在一些線性矩陣不等式（LMI）限制條件下，使系統的L_∞-gain性能的上界最小化。另外，我們提出了一種LMI- constrained進化演算法（EA）來有效地找到L_∞-gain性能的上界。因此，將非線性隨機L_∞-gain控制問題轉化為一個求解LMI的控制問題，可以通過Matlab程式簡單地解決。我們所提出的方法充分抑制了由於突然跳躍引起的狀態峰值，而且把L_∞-gain控制問題從非隨機系統延伸到隨機系統。最後，通過模擬驗證了本文的有效性。

To date, nonlinear stochastic L_∞-gain control problems have not been solved by conventional control methods for nonlinear dynamic systems with jump diffusion noise. In this paper, an L_∞-gain method is proposed to deal with the nonlinear stochastic control problem. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear dynamic system. Next, based on the fuzzy model, a fuzzy observer-based controller is developed to minimize the upper bound of the system's L_∞-gain performance under some linear matrix inequality (LMI) constraints. In addition, we propose an LMI-constrained evolution algorithm (EA) to efficiently find the upper bound of L_∞-gain performance. Therefore, the nonlinear stochastic L_∞-gain control problem is transformed to an LMI-based control problem which can be easily solved by Matlab toolbox. The proposed method, which sufficiently attenuates the peak of the state due to the sudden jump, extends the L_∞-gain control problems from non-stochastic systems to stochastic systems. Finally, a simulation is given to validate the effectiveness of this paper.

摘要--------------------------------------------------------------i
Abstract--------------------------------------------------------ii
誌謝------------------------------------------------------------iii
Contents--------------------------------------------------------iv
I INTRODUCTION------------------------------------------------1
II PROBLEM FORMULATION----------------------------------------2
III L_∞-gain FUZZY OBSERVER-BASED CONTROL DESIGN FOR NONLINEAR STOCHASTIC SYSTEMS-----------------------------------------------7
IV L_∞-gain FUZZY CONTROL DESIGN VIA LMI-CONSTRAINED EVOLUTION ALGORITHM-------------------------------------------------------15
V SIMULATION-------------------------------------------------19
VI CONCLUSIONS-----------------------------------------------24
REFERENCES------------------------------------------------------25

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