ENEE 769B Advanced Topics in Control: Geometric Methods in Control and Information

ENEE 769B - Geometric Methods in Control and Information

Spring 2006

Last Update 6:30 pm Wednesday, April 5, 2006

Course Information

Special Announcements

(9) 1964 Paper by Wei and Norman linked; 1975 paper by R.L. Bishop linked

(8) Lecture 5,6,7, and papers by Brockett and Howe posted.

(7) Lecture 3 pages 17-25, Lecture 4 pages 1-16 and Homework 3 posted. PSK on travel Feb 28- March 3. Bijan Afsari will lecture on double bracket equation and its use on March 1.

(6) Weblinks to Nelson's books posted. See especially the discussion on the kinematic car in the book on Tensor Analysis. See also corrections to Lecture 3 Notes.

(5) Additional lecture notes #2 (pages 25-27), homework 2, lecture notes #3 (pages 1-16) posted.

(4) Extra class on Monday, February 6 at 7:00 pm, A.V.Williams Bldg, room 2168 (ISR conference room)

(3) Homework Set 1 posted.

(2) Lecture 2 posted.

(1) Lecture 1 posted.

Weekly Lecture Notes by P. S. Krishnaprasad

Lecture 1 (pages 1-17); pages 18-19

Lecture 2 (pages 1-13 except page 2); page 2; pages 14 to 17(c); pages 18 to 24; pages 25 to 27 on the use of the pre-image theorem

Lecture 3 (vector fields); corrections to lecture 3; Lie algebras, one parameter transformation groups, unicycle example.

Lecture 4 (differential forms); pairing covector fields to vector fields using a Riemannian metric; the double bracket flow of Brockett;

Lecture 5 (Lie Groups)

Lecture 6 (overview lecture on control systems on Lie Groups)

Brockett's 1973 lectures (Lie groups and Lie algebras in control theory) pages 43 to 63; pages 64 to 81

Roger Howe's 1983 paper (Very basic Lie theory); corrections to Howe's paper (1984)

Lecture 7a (Frenet-Serret frame as a control system on SE(2)); Lecture 7b (Relatively parallel adapted frames)

Homework Assignments

Homework 1

Homework 2

Homework 3

Homework solutions:

Will be provided by email.

Some interesting resources on the web

Topics in Dynamics I: Flows by Edward Nelson

Tensor Analysis by Edward Nelson

Paper by Wei and Norman on product of exponentials representation

Paper by R.L. Bishop on relatively parallel adapted frames (or natural Frenet frames)

To be posted