Viability, Invariance and Applications pdf epub mobi txt 电子书下载 2026

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出版者:Elsevier Science Ltd

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

出品人:

页数:344

译者:

出版时间:2007-8

价格:$ 158.20

装帧:HRD

isbn号码:9780444527615

丛书系列:

图书标签:

控制理论
稳定性分析
不变性
Lyapunov方法
非线性系统
优化
应用数学
工程控制
系统辨识
自适应控制

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具体描述

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》是一部旨在为读者提供深入理解与实用知识的书籍。这本书以严谨的学术背景和丰富的理论研究著称，系统地探讨了概率模型、统计分析以及相关应用领域的重要性。内容涵盖了从基础概念到高级技术的全面内容，帮助读者建立坚实的理论知识体系。书中首先对可行性问题进行深入剖析，通过多维度分析解决实际问题中的挑战。作者详细阐述了在不同情境下评估可行性的方法和工具，使读者能够准确判断项目或方案的实现可能性。同时，书中还强调了如何从理论出发，为决策提供科学依据，从而提升效率和成功率。其次，本书深入探讨了不变性（invariance）这一核心概念，解析了在复杂系统中保持稳定性的重要性。这部分内容不仅为读者理解系统行为提供了关键视角，也展示了不变性在科学研究和工程实践中的广泛应用。通过大量实例和数据分析，作者展示了如何利用不变性原理优化设计和改进方法。《Viability, Invariance and Applications》不仅关注理论知识的传授，更注重其在实际操作中的运用。书中引入了多种案例研究，从经济学、生物学到工程技术，均有深入探讨。这些案例不仅丰富了内容，还为读者提供了具体应用的参考和启示，使他们能够将理论知识转化为实际成果。此外，本书还特别强调跨学科视角的融合，通过对比不同领域中的相似问题，帮助读者拓宽思维，提升综合分析能力。这种多学科交叉的思维方式是当前科研和应用研究中不可或缺的一部分。在结构设计上，书采用了清晰递进的章节安排，每一章都紧密联系，形成完整的学习路径。各章节内容经过精心梳理，使读者能够逐步理解与掌握复杂概念。同时，图表、例题和参考文献的合理运用，有助于增强可读性和学习效果。总体而言，这本书不仅为专业学者提供了深入研究的资源，更以易懂且丰富的内容帮助广大读者提升知识水平。在应用领域，它为各行各业带来了实用性的思路和方法论支持，具有广泛的适用价值。通过细致入微的内容设计和全面的覆盖，这本书将成为对学习与研究有深度参与者的重要参考资料，帮助他们更好地应对复杂问题，实现理论与实践的统一。