針對一個已知的非線性系統，提出一個線性二次最佳化學習控制的方法，在有限時間內達到最佳化控制的目的。雖然此系統會被不明但重覆的干擾所影響，但是此學習效果依然會達到最佳化。此方法在線性系統的限制是特徵值必須落在某個範圍，可以用極點安置的方式來加以改善。另一方面，將最佳線性化的方式使用在非線性系統，在每次疊代前，針對操作點產生相對應的最佳線性化的模型，再使用極點安置來移動特徵值，並結合線性二次最佳化學習控制，來設計非線性系統的控制器追蹤所預定的軌跡。在這篇論文中，以例子及模擬的結果來說明這個機制以及顯示出改善的狀況。

　　A linear quadratic optimal learning control solution to the problem of finding a finite-time optimal control history for a nonlinear system is proposed in my thesis. This mechanism without the detailed information of the system that is influenced by unknown but repetitive disturbances yields the learning to achieve optimization. But for the linear systems, it is restricted to the range of eigenspectrums, the absolute eigenvalues of the linear systems. In order to improve the mechanism for more linear systems, the technique of pole placement is used. In the other hand, optimal linearization technique is used for the nonlinear systems. Before starting every iteration, we produce the relative optimal linear model at the operating point. Then, we design the controller of nonlinear systems to track the designed trajectories with linear quadratic learning control that is modified by pole placement. Illustrative examples and the results of simulation are proposed in my thesis to illustrate the mechanism and show how the improvement about the idea is.

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