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Mathematical Sciences: Nonlinear Differential Equations and Control; High Order Homogeneous Approximations

数学科学：非线性微分方程与控制；

基本信息

批准号：
9100439
负责人：
Henry Hermes
金额：
$ 3万
依托单位：
University of Colorado at Boulder
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1991
资助国家：
美国
起止时间：
1991-08-01 至 1994-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100439&HistoricalAwards=false
关键词：
Mathematical Sciences Nonlinear Differential Equations

项目摘要

In this project the principal investigator will continue his study of vector fields that are homogeneous with respect to a dilation in order to apply these results to the approximation of solutions of nonlinear differential equations and control systems. In particular, he will study the existence of asymptotically stabilizing feedback controls for nonlinear systems via homogeneous approximations, and then he will attempt to construct such feedback controls for systems that are small- time locally controllable about their uncontrolled rest state. The construction of asymptotically stabilizing feedback controls remains one of the fundamental problems of control theory. Control systems are a common feature of modern everyday life. Think of the thermostat in your home that controls the furnace or the air-conditioner. Many of these control systems are governed by linear equations, and for them there is now an extensive and nearly complete theory. On the other hand, many technologically important control systems are nonlinear, that is, the process to be controlled is governed by a nonlinear equation or system of equations. For nonlinear control systems the theory is far from complete. In this project the principal investigator will seek approximate solutions of nonlinear control problems by means of sophisticated methods based upon linear system theory.

在这个项目中，首席研究员将继续研究相对于膨胀齐次的矢量场，以便将这些结果应用于非线性微分方程和控制系统的近似解。特别地，他将通过齐次逼近研究非线性系统渐近稳定反馈控制的存在性，然后他将尝试构造关于其不受控制的静止状态的小时间局部可控系统的反馈控制。渐近稳定反馈控制的构造一直是控制理论的基本问题之一。控制系统是现代日常生活的一个共同特征。想想家里控制炉子或空调的恒温器。许多这样的控制系统是由线性方程控制的，对于它们现在有一个广泛的和几乎完整的理论。另一方面，许多技术上重要的控制系统是非线性的，也就是说，被控制的过程是由一个非线性方程或方程组控制的。对于非线性控制系统，这一理论还远远不够完善。在这个项目中，主要研究者将利用基于线性系统理论的复杂方法寻求非线性控制问题的近似解。