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Lyapunov函数，广义差异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类的非线性动力学系统的高度创新稳定理论开发高度创新的稳定理论。最终的目标是提供大胆而深远的统一，对随时间变化的反馈稳定器和Lyapunov功能的各种现有构建体提供，该构建机将适用于具有离散和连续时间尺度和输出的混合物的非常通用的系统，包括非人性化系统，这些系统，这些系统，这些系统的混合连续时间不变的反馈无法在全球范围内稳定。这样的系统在科学中无处不在。 要提出的其他主题包括（a）量化反馈延迟到先验稳定的闭环系统中的效果，（b）分析不连续反馈的分叉点，（c）跟踪具有不确定模型参数的工程模型的跟踪问题，（D） ）lyapunov函数的显式结构和具有测量不确定性的系统的平滑反馈稳定器，以及（e）准时间最佳反馈稳定。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的，系统的和用户友好的方法在许多学科中分析大量重要的稳定问题是可能的。数学控制理论和优化提供了理论基础，这些基础是构成许多基础，这些基础是许多人现代技术，包括航空技术，生物技术，通信网络，制造业和气候变化模型。反馈稳定在许多领域都使用，从机电工程到生物护理学。这个创新的项目将努力寻求突破，而不是逐步改进。它的方法将导致对重要类别的控制系统的反馈稳定器，这些控制系统超出了已知的连续反馈稳定技术的范围，但通常在工程中出现，例如具有时间延迟的系统和只有部分信息的多个时间尺度。该项目将在几种引人入胜的工程感兴趣的应用中建议并探索创意和原始反馈概念，例如化学固醇（这些模型的微生物建模以竞争限制营养成分）和微电机械继电器（用于在电动电路机中打开或密切连接）。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。这项工作将在传统上吸引许多少数族裔的机构进行，并将为招募人数不足的团体的合格研究助理而做出特殊努力。