Functional Automatic Differentiation with Dirac Impulses

Speaker: Henrik Nilsson, Yale University

When & Where:

12:30pm, Friday, April 11, 2003, Room 400 AKW


Functional Reactive Programming (FRP) is a framework for reactive programming in a functional setting. FRP has been applied to a number of domains, such as graphical animation, graphical user interfaces, robotics, and computer vision. Recently, we have been interested in applying FRP-like principles to hybrid modeling and simulation of physical systems. As a step in that direction, we have extended an existing FRP implementation, Yampa, in two new ways that makes it possible to express certain models in a very natural way, and reduces the amount of work needed to put modeling equations into a suitable form for simulation. First, we have added a notion Dirac impulses that allows certain types of discontinuities to be handled in an easy yet rigorous manner. Second, we have adapted automatic differentiation to the setting of Yampa, and generalized it two work correctly with Dirac impulses. This allows derivatives of piecewise continuous signals to be well-defined at all points. This talk reviews the basic ideas behind automatic differentiation, in particular Jerzy Karczmarczuk's elegant version for a lazy functional language with overloading, and then considers the integration with Yampa and the addition of Dirac impulses.