本論文所提出之複合控制器主要涵蓋H∞最佳化控制、倒傳遞類神經網路補償以及滑動控制律。首先推導出一個n階誤差方程式，並藉由H∞控制理論求得其參數。將動態誤差定義成滑動面，其參數以H∞方法求得，並將滑動面設為代價方程式，藉由倒傳遞類神經網路將代價方程式最小化並補償(u_NNi )至系統。如此，儘管系統含有不確定性與外部干擾，仍可以改善追蹤性能。為保證系統追蹤輸入訊號，根據第i個滑動面(S_i )及其一階導數(S ̇_i)之乘積為負定之條件，取得滑動控制參數。此外，以飽和函數取代sign函數，以消除滑動控制中震顫的現象，確保控制力的平滑。利用圓定理分析不確定性與未模型化之系統動態，以確保閉迴路系統之強健性。最後，以一機械手臂來驗證此控制器之可行性。對於含有未模型化之不確定性的非線性系統，在模擬結果中仍可看到良好的追蹤性能，以及此控制器的實用性。

In this paper, the H∞ - control optimization, the back propagation neural compensation and the sliding mode control law form there main components of the proposed composited controller. The proposed controller is first formulated into an n-th - order error equation form, whose parameters are then selected by the H∞ - optimization problem. The sliding surface, defined from the error dynamics, whose parameters are assigned by H∞ - methodology, is then set to be the cost function which is to be minimized by the proposed compensation of back propagation neural network (u_NNi) so that the tracking performance can be improved, even if the system encountered by plant uncertainties and disturbances. To ensure the asymptotical tracking of the commend inputs, the control parameters of the sliding mode control component are obtained in such a way that the product of the i-th sliding surface (S_i) and the first derivative of the i-th sliding surface (S ̇_i) is guaranteed to be negative. Besides, to remove the chattering effect in sliding-mode control law, the sign function is replace by the saturation function in the proposed composite controller to ensure the smoothness of the proposed control methodology. To handle the unmodeled uncanceled dynamics, the circle criterion is then utilized to ensure the robustness of the closed - loop system. Finally, a robot manipulator is used to demonstrate the feasibility of the proposed H∞ neural - sliding - mode composite controller. The good tracking performance shown in the simulation results clearly reveal that the proposed control structure is practical even for those nonlinear systems with unmodeled uncertainties.

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