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

摘要：非线性控制系统理论研究：Lyapunov函数、稳定与工程应用本研究将在数学控制理论中提供新的基于Lyapunov的稳定方法，该方法基于广义微分、最优控制和输入到状态稳定框架的系统使用。特别是，该项目将推导并应用新的反馈稳定技术，用于现有理论无法处理的流形上的非自治系统和欠驱动机械系统。其他相关的研究方向包括：a)时变控制-Lyapunov函数的显式构造，b)不连续反馈的分岔点分析，c) Lyapunov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。通过开发强大的新工程和数学技术，该项目将使使用单一的、系统的、用户友好的方法分析跨许多学科的大量重要稳定性问题成为可能。反馈稳定在许多领域都有应用，包括工程（例如，用于军事监视和侦察任务的自主空中和水面车辆的控制）和系统生物学（例如，病毒感染模型中的细胞受体分析）。该研究将通过支持研究生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项目方法。该项目将在一个传统上吸引许多少数民族的机构中进行，并将作出特别努力，从代表性不足的群体中征聘研究助理。

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.