在實際的非線性系統中，常含有參數不確定性、未模式化擾動及可能受到各種外擾影響，而造成控制性能下降，使得系統輸出響應不如預期。適應控制藉由參數調整器來自動調整控制參數，雖能克服系統含有參數不確定性的困擾，但無法排除外來干擾所帶來的不良影響。因為當系統受到外擾影響或回授訊號摻含有雜訊時，可能使參數調整器誤以為追蹤誤差變小，而停止控制參數的調整，導致閉迴路系統不穩定。

因此，本文將對非線性多變數系統，設計一個含有可變結構控制(VSC)之適應-H∞綜合控制器：以適應估測法則來估測系統未知或隨時間改變之參數，並利用可變結構控制器來消除未模式化擾動的影響，最後結合H∞控制器來提昇系統對外來干擾之強健性。

最後，本文以一具有未模式化擾動及受到外擾影響之質量-彈簧-阻尼系統，作為電腦模擬之控制對象，來驗證所設計之適應-H∞控制器之可行性。模擬的結果顯示，在適當的控制參數選取下，系統能有良好的追蹤性能，顯見所設計之適應-H∞控制器，確實能提高傳統適應控制之強健性。

Since a practical nonlinear system often has parameter uncertainties, unmodeled dynamics and external disturbances in it, the system performance is therefore hard to be achieved by using the traditional controllers. Adaptive control can overcome parameter uncertainties of systems by using parameter adjuster, but it can’t reject the influence of external disturbances. Because when a system has disturbances or has feedback signals containing sensor noises, the parameter adjuster may recognize by mistake that the tracking error was being diminished and stop to adjust the parameters, which may cause the closed loop system unstable.

In this study, an adaptive - H∞ control law, which contains variable -structural control algorithms, is derived for the nonlinear multiple-input multiple-output systems. The proposed control law adopts the adaptive algorithm to estimate the unknown or the time-varying parameters and uses the variable-structural controller to eliminate the influence of the unmodeled dynamics. Besides, by combining the H∞ control methodology, the proposed adaptive - H∞ controller can ensure the system robustness under the presence of external disturbances.

A mass-spring-damper system having unmodeled perturbation and external disturbances is studied in this research to attest the feasibility of the proposed adaptive - H∞ control design. The computer simulation results reveal that if the control parameters are properly chosen, the prescribed system performance can easily be achieved by the proposed adaptive - H∞ control methodology, which is robust to various system uncertainties.

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