Mathematical Sciences: Approximation of Singular Neutral Control Systems

数学科学：奇异中性控制系统的近似

• 批准号: 8907019
• 负责人: Janos Turi
• 金额: $ 0.85万
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-08-01 至 1990-07-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8907019&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Approximation; Singular; Neutral

This project involves the study of computational techniques for the approximation and control of systems governed by functional integro-differential equations of neutral type. Such systems arise in the modeling of certain aeroelastic control problems and include many singular integro-differential equations. The approach here is based upon a state-space formulation and makes use of approximation results in functional analytic semigroup theory to analyze the convergence of particular numerical schemes. The main objectives of this project are: (1) Select an "appropriate" state-space for singular neutral functional differential equations (SNFDE) and study the properties of the infinitesimal generator of the solution semigroup associated with the homogeneous SNFDE; (2) Develop a general approximation framework for SNFDEs on the state-space and analyze the convergence properties of semi- discretized (i.e., averaging projections and various spline schemes) and fully-discretized numerical schemes for the approximate solutions to the SNFDE; (3) Develop the duality theory for SNFDEs and discuss control and observation problems. **//

该项目涉及对由中性型函数积分微分方程控制的系统进行逼近和控制的计算技术的研究。 此类系统出现在某些气动弹性控制问题的建模中，并且包括许多奇异积分微分方程。 这里的方法基于状态空间公式，并利用泛函解析半群理论中的近似结果来分析特定数值格式的收敛性。 该项目的主要目标是：（1）为奇异中性泛函微分方程（SNFDE）选择一个“适当”的状态空间，并研究与齐次SNFDE相关的解半群的无穷小生成元的性质； (2) 开发状态空间上 SNFDE 的通用近似框架，并分析 SNFDE 近似解的半离散化（即平均投影和各种样条格式）和全离散数值格式的收敛特性； (3)发展SNFDE的对偶理论并讨论控制和观测问题。 **//