Operator Theory Arising from Systems Engineering

源于系统工程的算子理论

基本信息

  • 批准号:
    0400794
  • 负责人:
  • 金额:
    $ 25.24万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2004
  • 资助国家:
    美国
  • 起止时间:
    2004-07-01 至 2008-06-30
  • 项目状态:
    已结题

项目摘要

The research of this proposal is in functional analysis and operator theory related to engineering system theory. Many linear control problems can be phrased and studied in terms of matrix inequalities. These are formulated by a consideration of polynomials in noncommutative variables x. A basic result, due to the PI and obtained as part of his previous grant, is that every matrix positive noncommutative polynomial can be written as a sum of squares of noncommutative polynomials. In this proposal Helton will work on extending this theory, developing computer algorithms based on this theory, the analysis of such algorithms, and connections with other branches of mathematics. These are key optimization problems arising in designs of linear systems.The biggest advance in linear systems engineering during the 1990's is the realization that most linear control problems convert directly to matrix inequalities, abbreviated MIs. Many of these are badly behaved but a classical core of problems convert to linear matrix inequalities (LMIs) that are nicely behaved. Many different types of matrix inequalities have come up in the mathematics of the previous century, but the ones that dominate in engineering systems usually take the form of a polynomial or rational function of matrices being positive semidefinite. It is algebraic formulas like these that are programmed into modern computer packages in engineering. The goal of this project is to understand how one converts bad MIs to nice MIs. When is this possible?
本方案的研究方向是工程系统理论中的泛函分析和算子理论。 许多线性控制问题可以用矩阵不等式来描述和研究。 这些公式是通过考虑非交换变量x中的多项式来制定的。 一个基本的结果,由于PI和获得的一部分,他以前的赠款,是每一个矩阵积极的非交换多项式可以写为一个总和的平方非交换多项式。在这项建议赫尔顿将致力于扩展这一理论,开发计算机算法的基础上,这一理论,分析这种算法,并与其他分支的数学。 这些是线性系统设计中出现的关键优化问题。20世纪90年代线性系统工程的最大进步是认识到大多数线性控制问题直接转化为矩阵不等式(简称MI)。这些问题中有许多表现不好,但经典的核心问题转化为表现良好的线性矩阵不等式(LMI)。在上个世纪的数学中出现了许多不同类型的矩阵不等式,但在工程系统中占主导地位的矩阵不等式通常采用多项式或半正定矩阵的有理函数的形式。 正是像这样的代数公式被编程到现代计算机软件包中。这个项目的目标是了解如何将坏的MI转换为好的MI。 什么时候才有可能?

项目成果

期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
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J. William Helton其他文献

NonlinearH ∞ control theory for stable plants
Optimization over analytic functions whose founrier coefficients are constrained
  • DOI:
    10.1007/bf01203384
  • 发表时间:
    1995-12-01
  • 期刊:
  • 影响因子:
    0.900
  • 作者:
    J. William Helton;Orlando Merino;Trent E. Walker
  • 通讯作者:
    Trent E. Walker
The Hessian of a noncommutative polynomial has numerous negative eigenvalues
  • DOI:
    10.1007/s11854-007-0016-y
  • 发表时间:
    2007-08-01
  • 期刊:
  • 影响因子:
    0.900
  • 作者:
    Harry Dym;J. William Helton;Scott Mccullough
  • 通讯作者:
    Scott Mccullough
Factorization results related to shifts in an indefinite metric
Classification of all noncommutative polynomials whose Hessian has negative signature one and a noncommutative second fundamental form
  • DOI:
    10.1007/s11854-009-0017-0
  • 发表时间:
    2009-09-11
  • 期刊:
  • 影响因子:
    0.900
  • 作者:
    Harry Dym;Jeremy M. Greene;J. William Helton;Scott A. McCullough
  • 通讯作者:
    Scott A. McCullough

J. William Helton的其他文献

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{{ truncateString('J. William Helton', 18)}}的其他基金

Operator Theory Arising from Systems Engineering
源于系统工程的算子理论
  • 批准号:
    1500835
  • 财政年份:
    2015
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Operator Theory Arising from Systems Engineering
源于系统工程的算子理论
  • 批准号:
    1201498
  • 财政年份:
    2012
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
FRG: Collaborative Research: Semidefinite optimization and convex algebraic geometry
FRG:协作研究:半定优化和凸代数几何
  • 批准号:
    0757212
  • 财政年份:
    2008
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Standard Grant
Operator Theory Arising from Systems Engineering
源于系统工程的算子理论
  • 批准号:
    0700758
  • 财政年份:
    2007
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Operatory Theory and Systems Engineering
操作理论与系统工程
  • 批准号:
    0100576
  • 财政年份:
    2001
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Operator Theory and Systems Engineering
算子理论与系统工程
  • 批准号:
    9732891
  • 财政年份:
    1998
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Operator Theory and Systems Engineering
数学科学:算子理论与系统工程
  • 批准号:
    9501064
  • 财政年份:
    1995
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Operator Theory and Systems Engineering
数学科学:算子理论与系统工程
  • 批准号:
    9207740
  • 财政年份:
    1992
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Operator Theory and Communications Engineering
数学科学:算子理论与通信工程
  • 批准号:
    8902098
  • 财政年份:
    1989
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Conference on Functional Analysis andApplications
数学科学:泛函分析与应用会议
  • 批准号:
    8703163
  • 财政年份:
    1987
  • 资助金额:
    $ 25.24万
  • 项目类别:
    Standard Grant

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