CAREER: Robust Nonlinear Control: Problems and Challenges from Communication Networks

人们普遍认识到，线性控制律不足以解释许多物理系统所具有的严重非线性和不确定性。本项目将研究的这类系统的两个例子是欠驱动机械系统和通信网络。在过去的二十年中，设计具有鲁棒性的性能目标非线性控制器的问题引起了许多研究者的关注。该项目的第一阶段将继续研究我们早期工作中开始的具有动态不确定性的非线性系统，并进一步深入了解（输入）动态不确定性对可实现性能的固有限制。尽管在最近的非线性控制文献中有许多优雅的结果，但从实际的角度来看，它们在具有复杂互连结构的分散非线性系统中的直接应用似乎受到限制。在非线性输入状态稳定性（ISS）小增益定理的新框架的基础上，我们将开发用于重要类别的分散非线性系统的非线性反馈设计工具，并应用于通信网络。该项目的第二阶段是解决通信网络中一些有趣的非线性控制问题。硬饱和非线性和时变不确定传播延迟的研究将产生新的分散/非线性控制问题，作为第一阶段基础研究的应用。我们期望我们从非线性控制角度的贡献将增加国家科学基金会在这一活跃应用领域的现有投资。这一职业发展计划的教育内容与研究工作密切相关。我们将加强理工学院目前的控制课程，将“非线性”思维纳入以“线性”方法为重点的经典反馈控制课程，并开发基于网络的教育工具和教程。教育计划的具体目标包括：(1)开设一门新的研究生课程{\em非线性系统理论}，报告非线性系统和控制的最新发展；(2)设立鲁棒非线性控制实验室，进行研究和教学，加强本系在控制方面的活动；(3)提倡动手实验，让本科生参与研究型和应用型项目；(4)通过研讨会、讲习班和继续教育计划，与实践工程师进行技术转让和新理论传播的互动。

It is widely recognized that linear control laws are inadequate to account forsevere nonlinearities and uncertainties that many physical systems possess.Two examples of such systems, that will be studied in this project,are underactuated mechanical systems and communication networks.The issue of designing performance-aimed nonlinear controllerswith robustness to significant uncertainties has drawn attention ofmany researchers in the last 20 years.Phase I of this project will continue the study of nonlinear systems withdynamic uncertainties, initiated in our earlier work, and provide furtherinsights into the inherent limitations on achievable performancecaused by (input) dynamic uncertainties.Despite many elegant results in the recent literature of nonlinear control,their direct application to decentralized nonlinear systems with complexinterconnecting structures seems to be limited from a practical point of view. On the basis of the new framework of nonlinear ISS (input-to-state stability) small-gain theorems, we will develop nonlinear feedback design tools for important classes of decentralized nonlinear systemswith applications to communication networks.Phase II of this project is to address some interesting nonlinearcontrol problems in communication networks. The study of hard saturationnonlinearities and time-varying uncertain propagation delays in such systemswill generate new decentralized/nonlinear control problems as applicationsfor the basic research in Phase I.We expect that our contributions from the nonlinear control perspectivewill enhance the NSF's existing investment in this active application area.The educational element of this CAREER development plan is closely linked tothe research work. We will enhance the current control curriculum at Polytechnicby incorporating ``nonlinear'' thinking into the classical feedback control courses where ``linear'' methods are now the focal point, and by developing Web-based educational tools and tutorials.The specific goals of the educational plan include:(1) developing a new graduate course {\em Nonlinear Systems Theory}to report on recent developments in nonlinear systems and control;(2) setting up a Laboratory for Robust Nonlinear Control for research and education,which strengthens the Department's activities in control;(3) promoting hands-on experiments and involving undergraduate students in research-oriented and application-driven projects; and(4) developing interactions with practicing engineers for technology transfer and dissemination of new theory through seminars, workshops and continuing education programs.