Organizers:
Richard Murray, CaltechSpeakers:
William Shadwick, University of Waterloo and Fields Institute
Richard Murray, CaltechTraditionally, geometric nonlinear control theory has relied on the vector field interpretation of affine nonlinear control systems to provide a set of tools for studying the structural properties of nonlinear systems. Recently, there has been an increased interest in alternative formulations of the control problem, where control systems are modeled using one-forms instead of vector fields. Systems which are described using one-forms are a subset of a class of systems known as exterior differential systems. Although one-forms and vector fields are dual to one another, there are tools available in theory of exterior differential systems which have no simple counterpart in the traditional geometric framework.
William Shadwick, University of Waterloo and Fields Institute
Willem Sluis, Fields Institute
Philippe Martin, Centre Automatique et Systems and UC Santa Barbara
Over the past few years, the use of exterior differential systems for studying problems in control has given new and exciting insights into the use of differential geometry as a tool for understanding the structure of nonlinear systems. In fact, many problems, such as trajectory generation for nonlinear systems, appear to be more natural when studied in the context of exterior differential systems. Many recent results in control of driftless nonlinear systems and differential flatness of nonlinear systems have relied on these tools, and the renewed interest in this area is already generating new ideas and new approaches in other areas of nonlinear control theory, such as nilpotent approximation, behavioral descriptions of control systems, and control of Lagrangian systems.
In this workshop we present an introduction to the machinery of exterior differential systems and show how it can be used to solve challenging problems in nonlinear control theory. We focus almost exclusively on control systems, allowing a considerably gentler introduction to the subject that what is traditionally available in the literature.
Workshop outline and schedule
Workshop homepage
EDS homepage