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

eduardo Sontag，罗格斯大学/ Yuan Wang，佛罗里达大西洋大学合作研究：基于状态稳定输入的非线性控制分析与设计本项目涉及反馈控制理论的数学基础。总体目标是进一步开发系统分析工具，基于状态稳定性的输入和相关的可检测性、调节性和稳定性概念。要研究的课题包括误差稳定性测量的精确表征的制定，这是反馈调节的核心概念，稳定性的鲁棒性相对于在特定类别中变化的信号，以及控制律的重新设计，以降低其对观测误差的敏感性。控制论是研究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，工程师们建造了结合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制对象的相互作用是控制论的主题。控制问题的数学分析有助于理解可实现目标的基本限制，无论使用何种精确技术，以及设计最适合任何给定问题的算法。

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.