Trajectory Exploration for Nonlinear Control Systems

Dr. John Hauser, CDS Visiting Faculty, University of Colorado at Boulder

An agile aircraft in the hands of a skilled pilot and a highly skilled alpine skier are but two examples of what might be called high performance nonlinear control systems. These are systems where aggressive maneuvering is central and where the class of possible maneuvers is very much constrained by the nonlinear dynamics of the system.

In this talk, we will discuss techniques for exploring the trajectory space of such nonlinear control systems. A key tool is a nonlinear projection operator defined using a simple trajectory tracking controller. Such a projection operator may be used, for example, to show that the set of trajectories of a nonlinear control system is a Banach manifold that is as smooth as the system is.