本研究將針對多輸入多輸出(Multiple-Input-Multiple-Output，MIMO)
之非線性不確定系統，提出一個非線性適應-H∞控制器，用以增強其追蹤
效能並維持閉迴路系統的穩定性。大多數的系統都屬於非線性系統，當
中不可避免受到系統參數的擾動或各種外部干擾的影響，由於這些因素
的存在，很可能造成整個系統的控制性能下降而導致系統不穩定。因此
在本文中，非線性系統中的不確定項可藉由適應控制之演算法則來估
測，以克服參數的不確定性，並結合H∞最佳控制的方法，將系統轉化為
標準的H∞控制問題，其控制增益能夠以兩個黎卡迪方程式獲得，以確保
系統受到任何外來干擾時，仍具有一定的強健性。文中並運用了李爾普
諾夫(Lyapunov)定理證明，含不確定性的閉迴路系統當中未能完全被補償
之非線性不確定項只要在可容許的範圍之內，則閉迴路系統仍然能夠保
持強健穩定(Robust Stability)。
最後，舉出兩個範例進行電腦模擬來驗證本文所設計控制器之可行
性，例題一針對倒單擺系統並給予外部干擾為弦波，例題二以含有未模
式化擾動及外部干擾之質量-彈簧-阻尼系統作為控制對象，模擬結果中
顯示此適應-H∞控制器的設計結果，確實能夠有效地降低外部干擾對系統
的影響及其誤差，使得系統能夠達到良好的追蹤性能。

In this research, an adaptive-H∞ controller, which is based on multiple-input multiple-output uncertain nonlinear systems, is proposed to improve the system tracking performance while keeping the closed-loop system stable. Most of nonlinear systems are inevitably influenced by the parameter variations, or the external disturbances and the un-modeled dynamics, which may result in poor performance or system instability. In this paper, the uncertain nonlinear terms of nonlinear systems are estimated by adaptive algorithm and the nonlinear controller of system is formulated into the standard H∞-control problem form so that the controller gain can be attained by solving the Riccati equations obtained from the proposed H∞-control methodology. To ensure the robust stability for the uncontrolled uncertain nonlinearities in the closed-loop system, an inequality based on Lyapunov stability theorem is also proposed. Finally, two examples are presented to demonstrate the feasibility of the proposed adaptive-H∞ control structure. The simulation results reveal that the tracking errors are effectively controlled and the pre-specified performance can be satisfied while the system is encountered by parameter variations and disturbances.

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