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

该项目将为数学控制理论中的重要非线性动态系统开发高度创新的稳定理论，基于系统使用李雅普诺夫函数，广义微分和输入到状态稳定性框架。最终的目标是提供一个大胆的和深远的统一的各种现有的结构的时变反馈稳定器和李雅普诺夫函数，这将适用于非常一般的系统的离散和连续的时间尺度和输出的混合物，包括非完整系统，不能全局稳定的连续时不变反馈。这样的系统在科学中无处不在。 其他要研究的课题包括：（a）量化将反馈延迟引入先验稳定闭环系统的影响，（B）分析不连续反馈的分叉点，（c）具有不确定模型参数的工程模型的跟踪问题，（d）具有测量不确定性的系统的李雅普诺夫函数和光滑排斥反馈稳定器的显式构造，（e）拟时间最优反馈镇定。通过开发强大的新工程和数学技术，这项工作将使人们有可能使用一个单一的，系统的和用户友好的方法来分析跨学科的一大类重要的稳定性问题。数学控制理论和优化提供了支撑许多现代技术，包括航空，生物技术，通信网络，制造业和气候变化模型的理论基础。反馈稳定被用于许多这些领域，从机电工程到生物数学。这个创新项目将力求突破，而不是渐进式的改进。它的方法将导致反馈稳定器的显着类别的控制系统，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个时间尺度，只有部分信息是可用的。该项目将建议和探索具有引人注目的工程兴趣的几种应用中的创造性和原创性反馈概念，例如恒化器（模拟微生物竞争限制营养素）和微机电继电器（用于打开或关闭电路中的连接）。该研究将通过支持研究助理来促进学习，研究助理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群体的机构进行，并将作出特别努力，从代表人数不足的群体中征聘合格的研究助理。

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.