Shooting Methods for Locating Grazing Phenomena in Hybrid System

by

Professor Ian Hiskens

University of Wisconsin - Madison

Department of Electrical and Computer Engineering

Abstract - Hybrid systems are typified by strong coupling between continuous dynamics and discrete events. For such piecewise smooth systems, event triggering generally has a significant influence over subsequent system behavior. Therefore it is important to identify situations where a small change in parameter values alters the event triggering pattern. The bounding case, which separates regions of (generally) quite different dynamic behavior, is referred to as grazing. At a grazing point, the system trajectory makes tangential contact with an event triggering hyper surface. The conditions describing grazing points can be formulated as a boundary value problem, and solved using shooting methods that are applicable for general nonlinear hybrid (piecewise smooth) dynamical systems. The grazing point formulation underlies the development of a continuation process for exploring parametric dependence. It also provides the basis for an optimization technique that finds the smallest parameter change necessary to induce grazing. Examples will be drawn from power electronics, power systems and robotics, all of which involve intrinsic interactions between continuous dynamics and discrete events.

Friday, September 30, 2005

3:30 – 4:30p.m.

Rm. 1500 EECS