MSPA-ENG: Research in Nonlinear Control Systems Theory: Lyapunov Functions, Stabilization, and Engineering Applications II

MSPA-ENG：非线性控制系统理论研究：李雅普诺夫函数、稳定性和工程应用 II

• 批准号: 0708084
• 负责人: Michael Malisoff
• 金额: $ 18.79万
• 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: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708084&HistoricalAwards=false
• 关键词: MSPA; ENG; Research; Nonlinear; Control

This project will develop highly innovative stabilization theory for important classes of nonlinear dynamical systems in mathematical control theory, based on the systematic use of Lyapunov functions, generalized differentials, and the input-to-state stability framework. The ultimate goal is to provide a bold and far-reaching unification of the various existing constructions of time-varying feedback stabilizers and Lyapunov functions, which will apply to very general systems with mixtures of discrete and continuous time scales and outputs, including nonholonomic systems that cannot be globally stabilized by continuous time invariant feedbacks. Such systems are ubiquitous in science. Other topics to be pursued include (a) quantifying the effects of introducing feedback delays into a priori stable closed loop systems, (b) analysis of bifurcation points of discontinuous feedbacks, (c) tracking problems for engineering models with uncertain model parameters, (d) explicit constructions of Lyapunov functions and smooth repulsive feedback stabilizers for systems with measurement uncertainty, and (e) quasi time optimal feedback stabilization. By developing powerful new engineering and mathematical techniques, this work will make it possible to analyze a large class of important stability problems across many disciplines using a single, systematic and user-friendly approach.Mathematical control theory and optimization provide the theoretical foundations that undergird many modern technologies including aeronautics, biotechnology, communications networks, manufacturing, and models of climate change. Feedback stabilization is used in many of these areas, ranging from electromechanical engineering to biomathematics. This innovative project will strive for breakthroughs rather than incremental improvements. Its methods will lead to feedback stabilizers for significant classes of control systems that are beyond the scope of the known continuous feedback stabilization techniques but which commonly arise in engineering, such as systems with time delays and multiple time scales for which only partial information is available. This project will suggest and explore creative and original feedback concepts in several applications that are of compelling engineering interest, such as chemostats (which model microorganisms competing for limiting nutrients) and micro-electromechanical relays (which are used to open or close connections in electric circuits). The research will promote learning by supporting research assistants, who will apply and validate the methods in a control system laboratory. The work will be carried out at an institution that traditionally attracts many minorities, and special efforts will be made to recruit qualified research assistants from under-represented groups.

该项目将基于李雅普诺夫函数、广义微分和输入到状态稳定性框架的系统使用，为数学控制理论中重要的非线性动力系统类开发高度创新的稳定理论。最终目标是对现有的各种时变反馈稳定器和李雅普诺夫函数的结构进行大胆而深远的统一，这将适用于具有离散和连续时间尺度和输出混合的非常一般的系统，包括不能通过连续时不变反馈全局稳定的非完整系统。这样的系统在科学中无处不在。其他要研究的主题包括(a)量化将反馈延迟引入先验稳定闭环系统的影响，(b)不连续反馈的分岔点分析，(c)具有不确定模型参数的工程模型的跟踪问题，(d)具有测量不确定性系统的Lyapunov函数和光滑排斥反馈稳定器的显式构造，以及(e)准时间最优反馈稳定化。通过开发强大的新工程和数学技术，这项工作将使使用单一、系统和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。数学控制理论和优化为许多现代技术提供了理论基础，包括航空、生物技术、通信网络、制造业和气候变化模型。从机电工程到生物数学，反馈稳定技术在许多领域都有应用。这一创新项目将力求突破，而不是渐进式改进。它的方法将导致反馈稳定器的重要类别的控制系统，超出了已知的连续反馈稳定技术的范围，但通常出现在工程中，如系统的时间延迟和多时间尺度，只有部分信息是可用的。该项目将提出并探索在几个具有引人注目的工程兴趣的应用中具有创造性和原创性的反馈概念，例如化学调节器（模拟微生物竞争限制营养物质）和微机电继电器（用于打开或关闭电路中的连接）。这项研究将通过支持研究助理来促进学习，他们将在控制系统实验室中应用和验证这些方法。这项工作将在一个传统上吸引许多少数民族的机构进行，并将作出特别努力，从代表性不足的群体中征聘合格的研究助理。