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Backwards Reachability for Nonlinear, Nondeterministic Continuous Systems

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Abstract:
The application of the Hamilton-Jacobi (-Bellman) (-Isaacs) equation to optimal control and differential games has a lengthy history, but it is only recently that computing power and algorithms have developed to the point where accurate approximations can be determined for some nonlinear systems of practical interest. Previous work has demonstrated how the HJ equation can be used to compute the backward reachable set or tube for systems subject to control and uncertainty, but in limited dimensions. In this talk I will demonstrate a new formulation which may double the dimension of systems for which these schemes are practical, as well as demonstrate several applications in aircraft control. The algorithms used are not trivial to implement, but I will describe a Toolbox of Level Set Methods (available at my web site) which is written entirely in Matlab and which includes code and examples for most of the described techniques.

Type of Seminar:
IfA Seminar
Speaker:
Prof. Ian Mitchell
Department of Computer Science, University of British Columbia, Vancouver
Date/Time:
Nov 02, 2010   15:00
Location:

ETZ Gloriastrasse 35, H 91
Contact Person:

John Lygeros
File Download:

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Biographical Sketch:
Ian M. Mitchell received a B.A.Sc. in Engineering Physics and an M.Sc. in Computer Science from the University of British Columbia, Canada in 1994 and 1997 respectively, and a Ph.D. in Scientific Computing and Computational Mathematics from Stanford University in 2002. While at Stanford, he spent the summer of 1999 as the SIAM/AAAS Mass Media Fellow at the Chicago Tribune newspaper, writing about technology on the business desk. After spending a year as a postdoctoral researcher in the Department of Electrical Engineering and Computer Science at the University of California, Berkeley and the Department of Computer Science at Stanford, Dr. Mitchell joined the faculty in the Department of Computer Science at the University of British Columbia where he is now an associate professor. He is the author of the Toolbox of Level Set Methods, the first publicly available high accuracy implementation of solvers for dynamic implicit surfaces and the time dependent Hamilton-Jacobi equation that works in arbitrary dimension. His research interests include scientific computing, hybrid systems, verification, robot path planning and reproducible research.