Collaborative Research: Nonlinear Control Analysis and Design Based on Input to State Stability

DMS-0504557/DMS-0504296罗格斯大学/佛罗里达大西洋大学的Eduardo Sontag合作研究：基于对状态稳定性的输入的非线性控制分析和设计本项目涉及反馈控制理论的数学基础。总体目标是基于对状态稳定性的输入以及可检测性、调节和稳定性的相关概念，进一步开发系统分析工具。其中要研究的主题包括对误差稳定性测量的精确表征的表述，这是反馈调节的核心概念，针对特定类别变化的信号的稳定性的稳健性，以及重新设计控制律以降低其对观测误差的敏感性。控制理论是处理控制系统分析和设计的基本原理的领域。控制一个对象意味着影响它的行为，以达到预期的目标。为了实现这种影响，工程师们建造了融合了各种数学技术的设备。这些设备的范围从瓦特在英国工业革命期间设计的蒸汽机调速器，到CD播放机和汽车、工业机器人、飞机自动驾驶仪、电网和通信网络等消费品中的复杂计算机控制器。研究这些装置及其与被控对象的相互作用是控制理论的主题。对控制问题的数学分析有助于理解在设计最适合于任何给定问题的算法时，无论使用什么精确技术，对可实现的东西都有基本的限制。

Award Abstract DMS-0504557 / DMS-0504296Eduardo Sontag, Rutgers University / Yuan Wang, Florida Atlantic UniversityCollaborative Research: Nonlinear Control Analysis and Design Based on Input to State Stability This project deals with mathematical foundations of feedback control theory. The overall goal is to further develop systems analysis tools, based on input to state stability and related notions of detectability, regulation, and stabilization. Among the subjects to be studied are the formulation of precise characterizations of measurement to error stability, which is a notion central to feedback regulation, the robustness of stability with respect to signals that vary in specific classes, and the redesign of control laws so as to decrease their sensitivity to observation errors.Control theory is the field that deals with the basic principles underlying the analysis and design of control systems. To control an object means to influence its behavior so as to achieve a desired goal. In order to implement this influence, engineers build devices that incorporate various mathematical techniques. These devices range from Watt's steam engine governor, designed during the English Industrial Revolution, to the sophisticated computer controllers found in consumer items such as CD players and automobiles, inindustrial robots, airplane autopilots, power grids, and communication networks. The study of these devices and their interaction with the object being controlled is the subject of control theory. Mathematical analysis of control problems helps understand fundamental limitations on what is achievable, irrespective of the precise technology being used, as well in the design of algorithms most appropriate for any given problem.