Sensitivity Analysis of the Set of Sustainable Thresholds

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2024-05-29 DOI:10.1007/s11228-024-00721-7

Pedro Gajardo, Thomas Guilmeau, Cristopher Hermosilla

引用次数: 0

Abstract

In the context of constrained control-systems, the Set of Sustainable Thresholds plays in a sense the role of a dual object to the so-called Viability Kernel, because it describes all the thresholds that must be satisfied by the state of the system along a time interval, for a prescribed initial condition. This work aims at analyzing the sensitivity of the Set of Sustainable Thresholds, when it is seen as a set-valued map that depends on the initial position. In this regard, we investigate semicontinuity and Lipschitz continuity properties of this mapping, and we also study several contexts when the Set of Sustainable Thresholds is convex-valued.

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一组可持续阈值的敏感性分析

在受限控制系统中，"可持续阈值集 "在某种意义上扮演着所谓 "可行性内核"（Viability Kernel）的双重角色，因为它描述了在规定的初始条件下，系统状态在时间间隔内必须满足的所有阈值。本研究旨在分析 "可持续阈值集 "的敏感性，当它被视为一个取决于初始位置的集合值映射时。为此，我们研究了该映射的半连续性和 Lipschitz 连续性属性，还研究了可持续阈值集为凸值时的几种情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.