Research in Nonlinear Control Systems Theory: Lyapunov Functions, Stabilization, and Engineering Applications

非线性控制系统理论研究：李亚普诺夫函数、稳定性和工程应用

• 批准号: 0424011
• 负责人: Michael Malisoff
• 金额: $ 17.11万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-15 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0424011&HistoricalAwards=false
• 关键词: Research; Nonlinear; Control; Systems; Theory

Abstract DMS-0424011, MalisoffLouisiana State UniversityResearch in Nonlinear Control Systems Theory: Lyapunov Functions, Stabilization, andEngineering ApplicationsThis research will provide new Lyapunov-based stability methods inmathematical control theory, which are based on the systematic use ofgeneralized differentials, optimal control, and the input-to-statestability framework. In particular, the project will derive and apply newfeedback stabilization techniques for nonautonomous systems andunderactuated mechanical systems on manifolds that are not tractable bythe existing theory. Other related lines of research to be pursuedinclude: a) the explicit construction of time-varying control-Lyapunovfunctions, b) the analysis of bifurcation points of discontinuousfeedbacks, c) approximation and regularity theory for Lyapunov functions,and d) the construction of state estimators for output stable systems.By developing powerful new engineering and mathematical techniques, thisproject will make it possible to analyze a large class of importantstability problems across many disciplines using a single, systematic,user-friendly approach. Feedback stabilization is used in many areas,including engineering (e.g., control of autonomous air and surfacevehicles for military surveillance and reconnaissance missions) andsystems biology (e.g., analysis of cell receptors in models of viralinfection). The research will promote learning by supporting graduatestudent research assistants, who will apply and validate the projectmethods in a mechanical engineering control system laboratory. The projectwill be carried out in an institution that traditionally attracts manyminorities, and special efforts will be made to recruit researchassistants from under-represented groups.

摘要DMS-0424011，Malisoff路易斯安那州立大学非线性控制系统理论研究：李雅普诺夫函数，稳定化和工程应用本研究将提供新的基于李雅普诺夫的稳定性方法在数学控制理论，这是基于系统使用广义微分，最优控制，和输入到状态稳定性框架。特别是，该项目将推导和应用新的反馈稳定技术的非自治系统和欠驱动的机械系统的流形上是不听话的现有理论。其他相关的研究领域包括：a）时变控制李雅普诺夫函数的显式构造，B）不连续反馈的分叉点分析，c）李雅普诺夫函数的逼近和正则性理论，d）输出稳定系统的状态估计器的构造。通过发展强大的新工程和数学技术，这个项目将使人们有可能分析一个大类的重要的稳定性问题，在许多学科使用一个单一的，系统的，用户友好的方法。反馈稳定用于许多领域，包括工程（例如，用于军事监视和侦察任务的自主空中和地面交通工具的控制）和系统生物学（例如，病毒感染模型中细胞受体的分析）。本研究将通过支持研究生研究助理来促进学习，研究生研究助理将在机械工程控制系统实验室应用和验证项目方法。该项目可以在一个传统上吸引许多少数群体的机构中进行，并将作出特别努力，从代表性不足的群体中招聘研究助理。