Ian Mitchell
Courses
Courses numbered 5xx are graduate level. Courses numbered 4xx and
below are undergraduate. A note to UBC students: as of the last time
I checked, you could count up to two courses from the other category
toward your degree (eg grad courses for undergraduates, ugrad courses
for grad students). Check with your advisor and the instructor for
permission. I am generally quite happy to have students take courses
at either level.
I try to keep the graduate course links live, but the undergraduate
course links for older courses may point to more recent offerings.
- 2011-2012:
- 2010-2011:
- 2009-2010:
- 2008-2009:
- Spring: CPSC
303 Numerical Approximation and Discretization (in WebCT Vista).
Although I would prefer to make most of the website publicly visible,
because of Vista's limitations you will not be able to access the
website unless you are registered for the course. If you would like
to get an idea about what the course will cover without registering,
you can look at
the 2007-2008 web
page, which had very similar material.
- Fall: CPSC 513 Integrated Systems Design: Introduction to Formal Verification.
- 2007-2008:
- 2006-2007:
- 2005-2006:
- 2004-2005:
- 2003-2004:
Reproducible Research
- The
workshop Reproducible
Research: Tools & Strategies for Scientific Computing was held
July 13-15, 2011 at UBC in coordination with the Applied Mathematics
Perspectives series of ICIAM 2011 satellite meetings.
- The talks were recorded and are available
as streaming
videos (the current format
requires Silverlight; let
me know if you require a different format).
- The organizers are currently investigating the possibility of a
special issue on reproducible research in the computational and data
sciences; stay tuned for more information.
Research
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My research agenda includes:
- Algorithms for designing and analyzing hybrid and embedded
systems.
- Level set algorithms for time-dependent Hamilton-Jacobi partial
differential equations (PDEs).
- Single pass (FMM, OUM) and sweeping algorithms for static
Hamilton-Jacobi PDEs.
- High quality, publically released implementations of these
algorithms.
- Application of these algorithms to path planning for autonomous
and semi-autonomous systems.
For those interested in experimenting with Level Set Methods for
solving time-dependent Hamilton-Jacobi PDEs, such as those that arise
in dynamic implicit surfaces and reachability, I have released:
.
I do not yet have any public code for direct approximation of
static (time-independent) Hamilton-Jacobi PDEs, such as those that
arise in robotic path planning. However, here are some slides
discussing the relationship between path planning and Hamilton-Jacobi
PDEs, various classes of algorithms for approximating the resulting
PDEs, and a few extensions on which I have worked:
Dynamic Programming Algorithms for
Planning and Robotics in Continuous Domains and the Hamilton-Jacobi
Equation. These slides were presented at
the Fast
Marching Method: Theoretical Underpinnings and Applications to
Robotics tutorial at IROS
2008.
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Selected publications:
Many of my academic publications are available online.
Where permitted by the
publishers, I have provided links to self-archived post-prints (if
I have one) as well as the published versions (the latter usually
require subscriptions). If the paper you want is not hyperlinked or
if you are unable to access the publisher's web site, please email me
and I may be able to provide a copy by other means.
Journals
- "An Ordered Upwind Method with Precomputed Stencil and Monotone Node Acceptance for Solving Static Hamilton-Jacobi Equations."
Ken Alton and Ian M. Mitchell
Journal of Scientific Computing, online first.
- "Reproducible Research: Addressing the Need for Data and Code Sharing in Computational Science"
Yale Law School Roundtable on Data and Code Sharing
Computing in Science and Engineering, volume 12, number 5, pp. 8-13 (2010).
- The link above is to the open access published copy. In other
words, you should be able to get it for free. If you cannot, let me know.
- "Fast Marching Methods for Stationary Hamilton-Jacobi Equations with Axis-Aligned Anisotropy"
Ken Alton and Ian M. Mitchell
SIAM Journal of Numerical Analysis, volume 47, number 1, pp. 363-385.
- ©2008 Society for Industrial and Applied Mathematics.
- SIAM copy.
- "The Flexible, Extensible and Efficient Toolbox of Level Set Methods." (almost the version accepted for publication)
Ian M. Mitchell.
Journal of Scientific Computing, volume 35, numbers 2-3, pages 300-329 (June 2008).
- The only difference between the version linked above and the
version of the paper accepted for publication is that the version
linked above omits an appendix of tables containing the alpha-beta
parameters for the temporal integrator schemes from section 3.1.
Readers seeking those parameter values may find them in Spiteri &
Ruuth (citation [38]), the function odeCFLab in the code download
below, or in the Springer published version of this article.
- The published
version is available at SpringerLink.
- Code for the new features described in section 3: tarball or zipfile. Requires version 1.1
of the Toolbox of Level Set
Methods.
- Slides for the
related talk, providing a brief overview of the features of the
Toolbox version 1.1 (paper sections 2.1 - 2.3 & 2.5), some internal
design patterns used for flexibility and efficiency (paper section
2.4), the new SSP RK integrators and a new motion by mean curvature
scheme (paper section 3). This talk was first given at the International Conference on Industrial
and Applied Mathematics 2007.
- "Aircraft Autolander Safety Analysis Through Optimal Control-Based Reach Set Computation"
Alexandre M. Bayen, Ian M. Mitchell, Meeko M. K. Oishi and Claire J. Tomlin
AIAA Journal of Guidance, Control & Dynamics, volume 30, number 1, pages 68-77 (January-February 2007).
- Unfortunately, AIAA does not appear to permit self-archiving. If you are a member of AIAA, lobby them to allow self-archiving.
- Of course, there may be other places on the web where you can find the article.
- "Control Synthesis for State Constrained Systems and Obstacle Problems."
Alexander B. Kurzhanski, Ian M. Mitchell and Pravin Varaiya.
Journal of Optimization Theory and Applications, volume 128, number 3, pages 499-521 (March 2006).
- "Online Safety Calculations for Glideslope Recapture"
Jonathan Sprinkle, Aaron D. Ames, J. Mikael Eklund, Ian M. Mitchell and Shankar S. Sastry
Innovations in Systems and Software Engineering, volume 1, number 2, pp. 157-175 (July 2005).
- "A Time-Dependent Hamilton-Jacobi Formulation of Reachable Sets for Continuous Dynamic Games."
Ian M. Mitchell, Alexandre M. Bayen and Claire J. Tomlin.
IEEE Transactions on Automatic Control, volume 50, number 7, pages 947-957 (July 2005).
- ©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore copy
- "Overapproximating Reachable Sets by Hamilton-Jacobi Projections." (version accepted for publication)
Ian Mitchell and Claire Tomlin.
Journal of Scientific Computing, volume 19, number 1-3, pages 323-346 (December 2003).
- "Computational Techniques for the Verification of Hybrid Systems."
Claire Tomlin, Ian Mitchell, Alexandre Bayen and Meeko Oishi.
Proceedings of the IEEE, volume 91, number 7, pages 986-1001 (July 2003).
- ©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore copy
- The proof of the correctness of this formulation of reachable sets (at least for continuous systems) appears in Mitchell, Bayen & Tomlin, IEEE TAC 2005.
- "A Hybrid Particle Level Set Method for Improved Interface Capturing" (early draft)
Douglas Enright, Ronald Fedkiw, Joel Ferziger and Ian Mitchell.
Journal of Computational Physics, volume 183, number 1, pp. 83-116 (November 2002).
Single-Track Conferences
Multi-Track Conferences
- "Efficient Dynamic Programming for Optimal Multi-Location Robot Rendezvous"
Ken Alton and Ian M. Mitchell.
Proceedings of the Conference on Decision and Control, pp. 2794-2799 (December 2008).
- ©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore copy
- To see the conference talk, visit Ken Alton's web page.
- "Level Set Methods for Computing Reachable Sets of Systems with Differential Algebraic Equation Dynamics"
Elizabeth Ann Cross and Ian M. Mitchell.
Proceedings of the American Control Conference, pp. 2260-2265 (June 2008).
- "Multiple Aircraft Deconflicted Path Planning with Weather Avoidance Constraints"
Jessica J. Pannequin, Alexandre M. Bayen, Ian M. Mitchell, Hoam Chung & Shankar Sastry
Proceedings of the AIAA Guidance, Navigation, and Control Conference (August 2007).
- Unfortunately, AIAA does not appear to permit self-archiving. It looks like copies can be ordered from AIAA's publications web site, but my institution does not subscribe so I cannot verify that fact. If you are a member of AIAA, lobby them to allow self-archiving.
- Of course, there may be other places on the web where you can find the article.
- "Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation"
Meeko Oishi, Ian Mitchell, Claire Tomlin and Patrick Saint-Pierre.
Proceedings of the 45th IEEE Conference on Decision and Control, pages 3801-3807 (December 2006).
- ©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore copy
- IEEE Xplore AbstractPlus
- "Optimal Path Planning under Different Norms in Continuous State Spaces."
Ken Alton and Ian M. Mitchell.
Proceedings of the International Conference on Robotics and Automation, pp. 866-872 (May 2006).
- ©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore copy
- "Control Synthesis for State Constrained Systems and Obstacle Problems."
Alexander B. Kurzhanski, Ian M. Mitchell & Pravin Varaiya.
Proceedings of the IFAC Symposium on Nonlinear Control Systems (September 2004).
- "Continuous Path Planning with Multiple Constraints."
Ian M. Mitchell and Shankar Sastry.
Proceedings of the 42nd IEEE Conference on Decision and Control, pages 5502-5507 (December 2003).
- ©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore AbstractPlus
- An extended version is available as UC Berkeley Engineering Research Laboratory Technical Report UCB/ERL M03/34 (August 2003). Note that the equations in the appendix for T1 - T4, condition (5) and Pi(x0) are incorrect. We are presently (July 2007) in review on an extension which will fix these problems.
- "A Differential Game Formulation of Alert Levels in ETMS Data for High Altitude Traffic."
Alexandre Bayen, Shriram Santhanam, Ian Mitchell and Claire Tomlin.
Proceedings of the AIAA Guidance, Navigation, and Control Conference (August 2003).
- Unfortunately, AIAA does not appear to permit self-archiving. It looks like copies can be ordered from AIAA's publications web site, but my institution does not subscribe so I cannot verify that fact. If you are a member of AIAA, lobby them to allow self-archiving.
- Of course, there may be other places on the web where you can find the article.
- "Hybrid Verification of an Interface for an Automatic Landing."
Meeko Oishi, Ian Mitchell, Alexandre Bayen, Claire Tomlin and Asaf Degani.
Proceedings of the 41st IEEE Conference on Decision and Control, pp. 1607-1613 (December 2002).
- ©2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
- IEEE Xplore AbstractPlus
Technical Reports and Other Publications
Links
Local Research Groups:
Conferences and Workshops:
Useful Stuff:
- A list of directions for generating PDF
files from Windows using publicly available utilities.
- A collection of Matlab resources, with emphasis on links that can help beginners.
- The U.K. SHERPA RoMEO project, which collected and compares the publisher copyright policies for many technical societies and publishing houses.
- Many of the publishers that I deal with have quite reasonable self-archiving policies which permit authors to post some version of their papers; however, the details vary and can be quite specific. This project summarizes the policies and has links to the actual wording, which can be quite useful if you want to keep your website legal.
- For example, among the publishers that I have used, ACM, Elsevier, IEEE, SIAM, and Springer Verlag (including Kluwer) all get RoMEO green designations (the most author friendly designation). But remember to read the details of the publishers' policies before posting any copyrighted information.
- Authors: Support the publishers with liberal policies. Lobby the other publishers to follow suit. Government sponsored academic research is done for the common good, and while the publishers must support their editorial staff, they should not be permitted to govern all access to our results for eternity, thereby locking out those who cannot afford expensive subscription fees.
- SIAM has a web site and brochure
about careers in applied mathematics, of which scientific computing is
a huge component.
- Proceedings for Hybrid Systems Computation and Control: 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998
Postdoctoral Work
Doctoral Work
Created 19 August 2003.
Last updated 30 December 2011.
Created and maintained by Ian Mitchell.