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，非线性控制系统理论中的Malisofflouisiana州立大学研究：Lyapunov功能，稳定和工程应用程序这些研究将提供新的基于Lyapunov的稳定性方法中的稳定性方法，这些方法基于系统的系统使用，最佳差异，最佳差异，最佳控制，最佳差异，最佳控制理论 - 结构性框架。特别是，该项目将针对非自主系统进行新馈回稳定技术，并在现有理论无法探讨的流形上进行机械系统。其他相关的研究渠道包括：a）明确构建时变的控制 - 裂解功能，b）不连续反馈的分叉点的分析，c）lyapunov函数的近似和规律性理论，以及d）国家估计量的构建对于输出稳定的系统。通过开发强大的新工程和数学技术，ThisProject将可以使用单一的，系统的，用户友好的方法来分析许多学科的大量重要稳定问题。反馈稳定在许多领域都使用，包括工程（例如，控制自主空气和用于军事监视和侦察任务的表面车辆）AndSystems Biology（例如，在病毒置换模型中对细胞受体的分析）。这项研究将通过支持毕业的研究助理来促进学习，他们将在机械工程控制系统实验室中应用和验证这些项目。该项目将在传统上吸引许多界限的机构中进行，并将做出特别的努力来招募代表性不足的群体的研究人员。