某些非線性動力系統中都含有未知的元素諸如未知系統參數(unknown parameter)或系統內部改變的不確定性(uncertainty)，此因素很可能造成控制系統的工作性能下降，甚至造成閉迴路系統不穩定。除了不確定性因素外，我們尚考量隨時間變動的不確定輸入(uncertain input)的影響，對於此系統的不確定輸入因素會造成系統不確定輸出，而此類輸入和輸出會在一些區域上變動，這使得針對系統追蹤性能的目標不易達成。

因此，本文將針對非線性系統，設計一個非線性管限追蹤H∞控制器：利用非線性系統的管限理論，結合H∞控制器配合選擇權重函數的迴路整型方法，提昇系統對外來干擾及系統內部不確定性之強健性，並保有優越輸入輸出的管限能力。

最後，本文針對線性直流馬達系統及非線性倒單擺系統作為電腦模擬控制對象，來驗證所設計之輸入輸出管限追蹤H∞控制器之可行性，經由模擬結果顯示均可達到管限追蹤目的，證明確實能使系統有良好的追蹤性能，並能有效降低外來干擾及輸入不確定因素的影響。

A nonlinear dynamic system usually contains some uncertainties, such as unknown system parameters or uncertainties, which may make desired performance hard to be achieved or even cause the close-loop system unstable. Uncertain inputs of the system will give the system uncertain outputs although these inputs and outputs may be bounded in some neighborhoods, yet these uncertainties may make the objective of tracking performance hard to be achieved.

An H∞ control design of system tracking behavior in the sense of input-output spheres is proposed in this paper to ensure the system outputs are bounded in the desired output spheres while the uncertain system inputs are prescribed in input spheres. The loop-shaping technique is applied in the proposed design procedure to guarantee the system robustness against disturbances and uncertainties.

A DC-motor and a nonlinear inverted pendulum are studied as examples in this research to attest the feasibility of the proposed H∞ control design, which will guarantee the tracking behavior in the sense of input-output spheres. The computer simulation results reveal that the designed H∞ controllers in these two examples can achieve the desired objectives with good tracking performance by effectively rejecting the system disturbances and uncertainties in both systems.

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