Award Abstract DMS-0504557 / DMS-0504296 Eduardo Sontag, Rutgers University / Yuan Wang, Florida Atlantic University
Collaborative 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, in industrial 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.
