Abstract: Reachable set estimation for systems with continuous-valued states, such as hybrid systems, require an electronic representation of the set of reachable points. Often, ellipsoids are used to estimate reachable sets. Ellipsoids can be concisely stored in the computer and offer several computational benefits over other representations. This talk provides an introduction to reachable set estimation using ellipsoidal representations. The following topics are covered:

1. Definition of ellipsoidal sets and their representation in the computer;
2. Operations on ellipsoids, such as estimation of set intersection;
3. Estimation of the reachable set of points from an ellipsoidal initial condition set;
4. Computation of invariant sets using Linear Matrix Inequalities (LMI) and Lyapunov techniques.

James Kapinski received his B.S.E.E. and M.S.E.E. degrees from the University of Pittsburgh in 1996 and 1999, respectively, and his Ph.D. from Carnegie Mellon University in 2004. Since receiving his Ph.D., he has functioned as a consultant, working on software tools for model based embedded system design and analysis, pulsed power generators, and electromagnetic launchers. His clients include Curtiss-Wright Advanced Products and Systems Division, Rockwell Collins, and Mon Valley Power. He is currently a postdoctoral researcher in the ECE Department at CMU. His research interests include model based embedded system design and analysis, hybrid systems, optimal control, and power systems. Appointments: dcm@cs.cmu.edu