Viability, Invariance and Applications pdf epub mobi txt 電子書下載在線閱讀 2026

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出版者:Elsevier Science Ltd

作者:Carja, Ovidiu/ Necula, Mihai/ Vrabie, I. I.

出品人:

頁數:344

译者:

出版時間:2007-8

價格:$ 158.20

裝幀:HRD

isbn號碼:9780444527615

叢書系列:

圖書標籤:

控製理論
穩定性分析
不變性
Lyapunov方法
非綫性係統
優化
應用數學
工程控製
係統辨識
自適應控製

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具體描述

This book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. This title presents new concepts for multi-functions as the classical tangent vectors for functions. It provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions. It features clarifying examples, illustrations and numerous problems, completely and carefully solved. It illustrates the applications from theory into practice. It is written in very clear and elegant style.

《Viability, Invariance and Applications》是一部旨在為讀者提供深入理解與實用知識的書籍。這本書以嚴謹的學術背景和豐富的理論研究著稱，係統地探討瞭概率模型、統計分析以及相關應用領域的重要性。內容涵蓋瞭從基礎概念到高級技術的全麵內容，幫助讀者建立堅實的理論知識體係。書中首先對可行性問題進行深入剖析，通過多維度分析解決實際問題中的挑戰。作者詳細闡述瞭在不同情境下評估可行性的方法和工具，使讀者能夠準確判斷項目或方案的實現可能性。同時，書中還強調瞭如何從理論齣發，為決策提供科學依據，從而提升效率和成功率。其次，本書深入探討瞭不變性（invariance）這一核心概念，解析瞭在復雜係統中保持穩定性的重要性。這部分內容不僅為讀者理解係統行為提供瞭關鍵視角，也展示瞭不變性在科學研究和工程實踐中的廣泛應用。通過大量實例和數據分析，作者展示瞭如何利用不變性原理優化設計和改進方法。《Viability, Invariance and Applications》不僅關注理論知識的傳授，更注重其在實際操作中的運用。書中引入瞭多種案例研究，從經濟學、生物學到工程技術，均有深入探討。這些案例不僅豐富瞭內容，還為讀者提供瞭具體應用的參考和啓示，使他們能夠將理論知識轉化為實際成果。此外，本書還特彆強調跨學科視角的融閤，通過對比不同領域中的相似問題，幫助讀者拓寬思維，提升綜閤分析能力。這種多學科交叉的思維方式是當前科研和應用研究中不可或缺的一部分。在結構設計上，書采用瞭清晰遞進的章節安排，每一章都緊密聯係，形成完整的學習路徑。各章節內容經過精心梳理，使讀者能夠逐步理解與掌握復雜概念。同時，圖錶、例題和參考文獻的閤理運用，有助於增強可讀性和學習效果。總體而言，這本書不僅為專業學者提供瞭深入研究的資源，更以易懂且豐富的內容幫助廣大讀者提升知識水平。在應用領域，它為各行各業帶來瞭實用性的思路和方法論支持，具有廣泛的適用價值。通過細緻入微的內容設計和全麵的覆蓋，這本書將成為對學習與研究有深度參與者的重要參考資料，幫助他們更好地應對復雜問題，實現理論與實踐的統一。