Mathematical Sciences: Functional Analysis and the Robust Control of Distributed and Nonlinear Systems

这个项目是一项数学研究，应用于控制系统的设计。泛函分析和算子理论的各种方法将应用于涉及矩阵解析函数的问题，特别是这类函数的最优上确界范数逼近和多变量Nevanlinna-Pick插值问题。这里的结果与量的计算有关，这些量使人能够稳定具有参数或建模不确定性的系统，同时满足某些性能规范。将考虑非线性和线性系统，并适当注意在非线性情况下基本算符理论的发展。

This project is mathematical research that has applications to the design of control systems. A variety of methods from functional analysis and operator theory will be brought to bear on problems involving matrix-valued analytic functions, in particular optimal supremum norm approximation by such functions and multivariable Nevanlinna - Pick interpolation problems. Results here are relevant to the computation of quantities which enable one to stabilize systems with parameter or modeling uncertainty while at the same time meeting certain performance specifications. Nonlinear as well as linear systems will be considered, with due attention to development of the underlying operator theory in the nonlinear case.