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

人们普遍认为，线性控制律不足以解决许多物理系统所具有的严重的非线性和不确定性。本项目将研究两个这样的系统的例子，是欠驱动的机械系统和通信网络。设计性能的问题-在过去的20年里，对显著不确定性具有鲁棒性的目标非线性控制器引起了许多研究者的关注。将继续研究具有动态不确定性的非线性系统，在我们早期的工作中开始，并提供了进一步的见解的内在限制，可实现的性能（输入）的动态不确定性caused.Despite许多优雅的结果在最近的文献中的非线性控制，其直接应用到分散的非线性系统与复杂的互联结构似乎是有限的，从实际的角度来看。基于非线性输入-状态稳定性小增益定理的新框架，我们将为重要的几类分散非线性系统开发非线性反馈设计工具，并将其应用于通信网络，本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saturationnonlinearities和时变不确定的传播延迟在这样的systems的研究将产生新的分散/非线性控制问题作为applicationsfor基础研究在第一阶段。我们希望，我们的贡献从非线性控制perspectively将提高NSF的现有投资在这个活跃的应用area.The教育元素这个职业发展计划是紧密相连的研究工作。我们将通过将“非线性”思想融入到以“线性”方法为重点的经典反馈控制课程中，并通过开发基于网络的教育工具和教程，来加强理工学院现有的控制课程。教育计划的具体目标包括：（1）开发一门新的研究生课程《非线性系统理论》，报告非线性系统和控制的最新发展;（2）成立“鲁棒非线性控制实验室”作研究及教育用途，以加强本系在控制方面的工作;（3）鼓励学生进行实验，并让本科生参与研究及应用项目;以及（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传播新理论的互动。

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.