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

9404128 Mordukhovich/Ioffe这个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Banach空间中非光滑映射的广义微分的基本工具和演算，无穷维函数的开性、正则性和相关性质的微分刻画，以及非光滑分析在微分方程和包含、分布参数系统以及约束优化和控制理论中的稳定性和敏感性问题的最优控制中的广泛应用。非光滑分析涉及到一种微积分的发展，该微积分适合于分析不具有必要的光滑性的函数，这些性质允许应用标准的变分法。这项研究在很大程度上是由于非光滑微积分和变分分析在制造系统优化和控制中的重要应用。特别是，这项工作涉及不确定条件下的动力系统的极小极大设计，参数摄动下最优解的稳定性，以及约束分布参数系统的鲁棒控制。***

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. ***