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題 名 | Numerical Computation of Cross-Covariance Functionals for Linear Systems with Multiple Time Delays=多重時延線性系統之交互共變異的計算 |
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作 者 | 黃志豪; 蔡三元; 黃奇; | 書刊名 | 中國工程學刊 |
卷 期 | 21:4 1998.07[民87.07] |
頁 次 | 頁409-423 |
分類號 | 448.51 |
關鍵詞 | 交互共變異; 時間延遲; 線性系統; 誤差平方積分; Cross-covariance functionals; Time delay; Linear systems; Integral of squared error; |
語 文 | 英文(English) |
中文摘要 | 在線性系統的參數最適化與線性濾波最適化的問題中,經常遭遇 F(s)G(-s)ds此種形式之交互共變異的計算。本篇論文提出一種計算 多重同步時延線性系統之交互共變異之演算法。此一方法是將交互共變異的形 式轉式一對等的自相關共變異之形式,再依循前人所提出的二維轉移函數之部 份分式展開法的機制將其分解,再利用殘數定理求得交互共變異之值。所提的 方法將交互共變異之計算簡化為一多項式矩陣之反矩陣的符號運算和一有限階 數之實係數多項式的因式分解。此外,文中所提的演算法亦應用至多重非同步 時延之交互共變異的計算。此一應用是藉由內插入一些假想的時延項或是利用 分式近似法來調整時延項將時延項化為同步。最後以三個實例驗證所提的演算 法之效能。 |
英文摘要 | The problem of evaluating a cross-covariance functional of the form F(s)G(-s)ds arises, e.g., in parametric optimization of linear systems and in optimal linear filtering. In this paper, an algorithm is presented for computing cross-covariance functionals for linear systems with multiple commensurate time delays. The algorithm is based on converting a cross-covariance functional into an equivalent auto-covariance one. Then by utilizing an existing partial-fraction- expansion scheme for a class of two-dimensional rational transfer functions, the evaluation of a cross-covariance functional is reduced to the determination of symbolic inversion of a polynomial matrix and the spectral factorization of a finite-degree- real-coefficient polynomial. It is shown that the algorithm presented here can be extended to systems having non-commensurate time delays by either introducing fictitious delays or adjusting time delays with rational approximations such that the resulting delays are commensurate. In order to illustrate the effectiveness of the algorithm, several examples are provided. |
本系統中英文摘要資訊取自各篇刊載內容。