本論文鑑於最佳化控制的控制輸入訊號很高，因此提出一個利用sign function algorithm建構於最佳化控制基礎上，利用線性二次式調整器技術和具高增益特性去得到一個輸入飽和限制值，且具有良好的追蹤效能。將良好的控制輸入當作開迴路反覆學習控制器的第一代追蹤器，在第一代的訓練中即可得到不錯的效能，再經由學習控制法則的疊代可以使暫態和穩態都具有良好的追蹤效能，且能改善傳統反覆學習控制得代數收斂及輸入飽和限制值。另外，我們提出一個解決反覆學習控制法則不連續函數且不可微分的方法，利用泰勒級數展開式趨近一個不連續函數的正確值。最後，我們提出個多輸入多輸出的例子，說明我們所提出方法的可行性。

In view of the optimal control whose control input signal is very large in the thesis, we present a sign function algorithm based on the foundation of optimal control using linear quadratic regulator and high gain property to get an input saturation value, and supplies a good tracking performance. Then, take this good control input to be as first iteration of open loop iterative learning controller, it can get as well as performance in the first training iteration, and supplies a good tracking performance in both the transient and steady-state phase. Moreover, the method improves convergence and input saturation value in traditional iteration learning control. Besides, we present a method to overcome discontinuous and non-differentiable function in iterative learning control update rule, using Taylor series expansion to approach a correct value. Finally, MIMO numerical example is given to illustrate the effectiveness and the feasibility of the proposed method.

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