Mathematical Sciences: Applications of Infinite Dimensional Nonsmooth Analysis to Optimization and Control

数学科学：无限维非光滑分析在优化和控制中的应用

• 批准号: 9404128
• 负责人: Boris Mordukhovich
• 金额: $ 11.89万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404128&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Infinite; Dimensional

9404128 Mordukhovich/Ioffe This project is concerned with developing effective methods of infinite dimensional nonsmooth analysis and their applications to various problems in optimization and control theory. The main focus is on basic tools and calculus for generalized differentiation of nonsmooth mappings in Banach spaces, differential characterizations of openness, regularity, and related properties of infinite dimensional multifunctions, as well as on a broad spectrum of applications of nonsmooth analysis to optimal control of differential equations and inclusions, distributed parameter systems, and stability and sensitivity questions in constrained optimization and control theory. Nonsmooth analysis is concerned with the development of a calculus suitable for the analysis of functions which do not have the necessary smoothness properties that allow application of the standard calculus of variations. This investigation is largely motivated by important applications of nonsmooth calculus and variational analysis to problems arising in optimization and control of manufacturing systems. In particular, this work is related to minimax design of dynamical systems under uncertain conditions, stability of optimal solutions under parameter perturbations, and robust control of constrained distributed parameter systems. ***

[404128] Mordukhovich/Ioffe本项目致力于发展无限维非光滑分析的有效方法，并将其应用于优化和控制理论中的各种问题。主要集中在巴拿赫空间中非光滑映射的广义微分的基本工具和微积分，开度的微分特征，正则性和无限维多函数的相关性质，以及非光滑分析在微分方程和包含物的最优控制，分布参数系统，约束优化和控制理论中的稳定性和灵敏度问题的广泛应用。非光滑分析涉及到一种微积分的发展，这种微积分适合于分析那些不具备必要的光滑性质的函数，这些性质允许应用标准变分法。这项研究主要是由非光滑微积分和变分分析在制造系统优化和控制中出现的问题的重要应用所推动的。特别是，这项工作涉及不确定条件下动力系统的极大极小设计，参数扰动下最优解的稳定性，以及约束分布参数系统的鲁棒控制。＊＊＊