在非線性系統中，系統往往含有參數的不確定性、未模式化擾動以及還有可能受到各種外部干擾的影響，因而造成控制性能降低，該系統的性能很難透過傳統控制器來實現，使得系統輸出響應不如我們所預期。在這項研究中，本文將針對非線性多輸入多輸出系統(Multiple-Input -Multiple-Output (MIMO) System)，設計一具有可變結構之適應-H∞綜合控制器，其中包含可調增益和適應- 控制律以及可變結構部份。在本文研究中所提出的控制器，其可調增益矩陣值將藉由標準 控制問題求取，而不是任意選擇的方式，此設計方法，使得本文所提出來的控制器對於系統參數不確定性以及外來干擾所造成的影響更具有強健性，並且實現良好的追蹤性能。

由於可調增益的設計是利用 控制技能的方法，此設計方法將確保閉迴路系統的穩定性，當系統含有參數不確定性或外界干擾之影響時，皆能有效克服此問題，並且將使控制輸出(誤差訊號和控制能量)降到最低。最後，本文針對倒單擺系統以及質量-彈簧-阻尼系統，作為電腦模擬之控制對象，以證明控制器之可行性，在複合式控制器設計的過程中，適應- 控制律以及可變結構控制，再結合可調增益矩陣利用 -最佳化(optimal)的設計方法，由以上兩個例子的電腦模擬中，此複合式控制器的設計結果，的確能夠達到設計者所需的性能。

In a nonlinear system, it often has parameter uncertainties, unmodeled dynamics and external disturbances. The system performance is therefore hard to be achieved by using the traditional controllers. In this study, a composite design of variable-structure adaptive H∞-control, which contains adjustable gains, the adaptive-H∞ control law and the variable-structure control portion, is proposed for nonlinear multiple-input multiple-output systems. In this research, the adjustable gains in the proposed controller are formulated in the form of the standard H∞-control problem so that the gains can be chosen by H∞-control methodology instead of being arbitrarily chosen. The proposed controller is then more robust to plant uncertainties /disturbances and is able to achieve good tracking performance.

Since the adjustable gains are assigned by the H∞-control skills to ensure the closed-loop stability, the ill-effects of the plant uncertainties (or disturbances) on the control outputs (such as tracking error or control energies) will be minimized. An inverted pendulum system and a mass-spring-damper system are simulated by using the proposed controller to attest it's feasibility on nonlinear uncertain systems. The design processes in determining the H∞-optimal control gains and the adaptive sliding-mode type H∞-controllers of the proposed composite controller are given step by step in these two examples to achieve the desired performance.

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