Mathematical Sciences: Approximation of Singular Neutral Control Systems

这个项目涉及计算技术的研究 用于近似和控制系统， 中立型泛函积分微分方程 等 在对某些气动弹性控制进行建模时， 问题，并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，并利用近似结果在功能 分析半群理论来分析 特殊的数值模式。 其主要目标是 项目是：（1）选择一个“适当的”状态空间， 奇异中立型泛函微分方程（SNFDE）， 研究无穷小生成元的性质， 与齐次SNFDE相关联的解半群;（2） 为SNFDE开发一个通用的近似框架， 状态空间，并分析了半状态空间的收敛性质， 离散化（即，平均投影和各种样条 格式）和全离散数值格式的 近似解的SNFDE;（3）发展对偶 理论SNFDES和讨论控制和观测问题。 **//

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. **//