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題 名 | Optimization of Integral Functional with Constrained Differential Inclusions=最佳化具有微分包含之積分泛函 |
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作 者 | 洪春棋; 卜湘麟; 洪淑玲; 劉百川; | 書刊名 | 黃埔學報 |
卷 期 | 48 民94.03 |
頁 次 | 頁57-67 |
分類號 | 314.7 |
關鍵詞 | 廣義方向導數; 廣義梯度; 法向錐; 正則; 切向錐; Generalized directional derivative; Generalized gradients; Normal cone; Regularity; Tangent cone; |
語 文 | 英文(English) |
中文摘要 | 具有微分包含之積分泛函的極小化數學規劃問題,以數學模式表示如下:極小化I (x,u) = □ ƒ (t, x (t), □ (t)) dt,受限於□(t) ∈ F (t, x (t)) ⊂□, x (t) ∈ K (t) ⊂□與x ∈ □[a, b],上式可被推導等價於下列最佳化問題-(J) 極小化 I (x) = □ L (t, x (t), □ (t)) dt,受限於x ∈ □[a, b],I ≤ p < ∞,其中,L (t, x (t), □ (t)) = ƒ (t, x (t), □ (t)) + Ψ□ (x (t)) + Ψ□ (x (t))。我們將討論在沒有凸性及局部Lipschitzian假設下,最佳化Lagrangian問題 (J) 的必需條件,換言之,我們將求得最佳化問題 (J) 的解,使其滿足廣義 Euler-Lagrange 方程式,即存在一絕對連續函數 p: [a, b]→□ 滿足(□ (t), p (t)) ∈ ∂□ L(t, z (t), □(t)),for a.a. t ∈ [a, b]。本文以測度論,積分泛函,與非平滑分析(nonsmooth analysis)等技巧,探討有關Langrangian力學方面的物理研究,有效解決Lagrangian力學上奇異點的能量估計問題,而得到一個廣義的Euler-Lagrange方程式,尤其沒有convexity與局部Lipschitzian的假設,使得結論更具應用價值。而導出的最佳化解,可得到目標函數:L(t, x (t), □ (t)) 之極小值,可應用在國防航太科技的追蹤控制(tracking control)等方面的研究。 |
英文摘要 | The minimization of the integral functional I (x,u) = □ ƒ (t, x (t), □ (t)) dt with implicit constraints □(t) ∈ F (t, x (t)) ⊂□, x (t) ∈ K (t) ⊂□, and x ∈ □[a, b] may reduce to the problem-(J) minimize I (x) = □ L (t, x (t), □ (t)) dt, subject to x ∈ □[a, b], I ≤ p < ∞, with L (t, x (t), □ (t)) = ƒ (t, x (t), □ (t)) + Ψ□ (x (t)) + Ψ□ (x (t)). In this paper, we will investigate the problem (J) without the assumptions of convexity and the locally Lipschitzian condition for the Lagrangian L(t, x (t), □ (t)) in (J) and prove that the optimal solution of (J) satisfies the generalized Euler-Langrange equation. Thiat is , there exists an absolutely continuous function p defined on [a, b] to □ such that, (□ (t), p (t)) ∈ ∂□ L (t, z (t), □ (t)), for a.a. t ∈ [a, b]. |
本系統中英文摘要資訊取自各篇刊載內容。