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題名 | Solution of Two Point Boundary Value Problem by Modified Laguerre Polynomials and Application to Optimal Control of Linear Systems=利用修飾Laguerre多項式二點邊界值問題及線性系統最佳控制之應用 |
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作者姓名(中文) | 王茂齡; 陳坤濯; 張榮語; | 書刊名 | Journal of the Chinese Institute of Chemical Engineers |
卷期 | 17:3 1986.05[民75.05] |
頁次 | 頁167-171 |
分類號 | 460.02 |
關鍵詞 | 二點邊界值; 多項式; 控制; 線性系統; |
語文 | 英文(English) |
中文摘要 | 本文乃利用經修飾Laguerre多項式近似法來解線性非時變二點邊界值問題,在傳統之Laguerre多項式中額外加一個參數而成為修飾Laguerre多項式,在本文中,首先導出修飾Laguerre多項式之積分運算矩陣,同時將此積分運算矩陣於解狀態方程式,另外,使用修飾之Laguerre多項式特性,吾人可將二點邊界值問題化簡為容易解之初始值問題,由本文中試舉一線性問題之最佳控制,由計算結果得知,利用本文所倡導之方法比傳統之Laguerre polynomials來得好。 |
英文摘要 | The problem of two point boundary value problem of linear time invariant system is solved by the modified Laguerre polynomials. An additional parameter is introduced to the conventional Laguerre polynomials to form the modified Laguerre polynomials. The operational matrix for the integration of the modified Laguerre polynomials is derived and is applied to the solution of state equations. Using the characteristics of the modified Laguerre polynomials, the two point boundary value problem is reduced to the initial value problem which can be easily solved. An illustrative example of optimal control of a linear system is given. The computational results show that the present proposed method is much better than that of the coventional Laguerre polynomials. |
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