本論文旨在發展一套高精度數值運算法則，針對數據化線性二次式最佳控制理論中回授控制計算所產生之數值問題提供解決方法。傳統控制器設計必須經由系統鑑別對系統進行估測以掌握系統資訊，而後再進行控制器設計。在數據化回授控制器設計理論中，可以一組系統測試數據進行設計且將系統閉迴路極點置於一個半徑小於單位圓的圓形區域內，如此一來，並不再需要繁瑣的系統鑑別步驟，且保有優良的系統響應。然而，在此設計法中存在著由數值運算所造成的誤差，導致設計結果嚴重偏離。本方法藉由可任意指定精度大幅度降低運算誤差，使得後續的控制器設計程序得以進行。

A special numerical platform is devised to enable the computations of a data-based linear quadratic (DBLQ) synthesis to be conducted with arbitrary precision that may be required. The proposed DBLQ algorithm is developed so that a LQ feedback design to confine its closed-loop poles to lie inside a prescribed circular disk within the unit circle can be synthesized based sorely on the plant test data and without explicit knowledge of the plant model. The computations of the proposed DBLQ synthesis, however, may involve arithmetic precision that far exceed those that are normally available with existing numerical platforms. In the research, a special numerical platform is devised so that numerical computations may be conducted with any arithmetic precision that is specified.

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