AA
599D/EE 546
Manifolds and Geometry for Systems and Control
Manifolds and Geometry for Systems and Control
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AA
599D/EE 546 Manifolds and Geometry for Systems and Control |
Winter 2004
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Office Hours
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The video of the lecture for Feb. 27 is located at http://vger.aa.washington.edu/aa599d-feb27.zip and is 400M compressed, 500M uncompressed. The uncompressed file is in the same location with a .doc extension.
Lectures: T/TH 12-1:30pm, MEB 243
This course provides an introduction to the fundamentals of calculus on manifolds and group theory focusing on applications in robotics and control theory. We will begin with an overview of the use of differential geometry in control theory relative to other techniques and build a rigorous foundation from which current literature can be understood. Topics to be covered include: manifolds, tangent spaces and bundles, Lie algebras, groups and semi-groups, and coordinate versus coordinate-free representations. Applications that will be addressed are modeling of mechanical systems, potential fields, nonholonomic systems, and self-assembling systems.
Suggested prerequisites: EE510
Due date Assignment Solution HW #1 Soln #1 HW #2 Soln #2 HW #3 Soln #3 HW #4 Soln #4 Midterm Midterm soln HW #5, HW #5 revised Soln #5 HW #6 Soln #6 Final Exam Soln #6
Homework and Exam Policy
Collaboration on homework assignments is allowed. You may consult outside reference materials, other students, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writring. No collaboration is allowed on the midterm or the final exam.
Grading
The final grade will be based on homework, a midterm, and a final exam.
- Homework: 50%. There will be 8 homework assignments due at the beginning of class on Tuesdays. Each problem set will have about 13 problems. Three are required to be completed by everyone, and of the remaining ten, five must be completed. Late homework will not be accepted without prior permission from the instructor.
- Midterm: 25% The midterm will be on Thursday, Feb. 12 and will be an in-class exam.
- Final exam: 25% The final exam will most likely be a take-home exam. If it is in class, it will take place on Thursday March 18, 10:30-12:30pm.
Course Text
The required reading source for the course isJ. E. Marsden, T. Ratiu, and R. Abraham, Manifolds, Tensor Analysis, and Applications, 3ed., Springer-Verlag, 2003.Additional references that may be useful:
- W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed. Academic Press, 1986. text excerpts
- Anthony Bloch, Nonholonomic Mechanics and Control, Springer Verlag.
- V. Guilleman and A. Pollak, Differential Topology, Prentice-Hall, 1974.
- J. Milnor, Topology from the Differentiable Viewpoint, University Press of Virginia, 1965.
- B. Schutz, Geometrical Methods of Mathematical Physics, Cambridge University Press, 1980.
- M. Spivak, A Comprehensive Introduction to Differentiable Geometry, v. 1. Publish or Perish, 1970.
- F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, 1983.
Web page maintained by K. Morgansen (morgansn@u.washington.edu)
Last updated: 5-Jan-2004