APM405/505, Spring 2007
Special Topics:
Variational Methods, Control, and Systems
Faculty: M. Shillor
Office: 554 SEB
Phone: 248-370-3439
Email: shillor@oakland.edu
Class Time: TuTh 6:30-9:50 PM
There will be two 10-minute breaks at
7:30 PM and 8:30 PM.
Room: 386 SEB
Office Hours: Tuesday and Thursday
5:00 - 6:00
PM, or by
appointment.
Prerequisites: Good background in
Ordinary Diff. Equations and minimal familiarity with Partial
Differential Equations. Some experience with rigorous
mathematical proofs. We will prove the main theorems.
We will also present many examples.
The main text:
Constrained
Optimization in the Calculus of
Variations and Optimal Control Theory,
by John Gregory and Cantian Lin, Van Nostrand reinhold, New York, 1992
We will also use bits and pieces from
the following two books:
1.
Variational
Methoda in Optimization, by D. R. Smith, Dover
Publications, Mineola, New York, 1974
2.
Introduction
to the Calculus of Variations, by Hans Sagan, Dover Publications, Mineola, New York, 1969
(The 1992 republication).
However, you can get by with the main
book only. I will supply the rest.
Exam : Thursday,
June 7.
There will be no Final
Exam. The grade in this
course will
be based
on the collected homework and
the one exam. The homework will be assigned during
the classes and is due every Tuesday beginning of class.
In case the university is officially
closed
on a scheduled exam date, the exam
will be held on the next class date that the university is officially
open.
Grades: There is no fixed grading
scale in
this course; a conversion formula from your
percentage score to Oakland University grades will be determined at the
end of
the course.
course will receive a course grade of 0.0 in addition to any penalties imposed by the
Academic Conduct Committee.
Important Dates:
Tuesday May 8 - First
class.
June 18 - Last day for official
withdrawal
(W grade).
June 21 - Last class.
Discussion board and chat room for the course
Schedule: We will cover most of Constrained
Optimization, and some parts of the other two books.
May 8, Tuesday: Preliminaries, Ch.
1 of CO (Constrained
Optimization)
May 15, Tuesday: Sections 2.1 and 2.2, Basic theory of the Calculus of Variations
May 17, Thursday: Section 2.3, examples
May 22, Tuesday: Hamilon-Jacobi theory, Optimal Control -begining, Section 4.1
May 24, Thursday: Additional topics and examples from Mechanics- The Implicit Function Theorem,
May 31, Thursday: Observability, Controlability, and Control of ODEs systems
(An Introduction). To download the pdf file of the lecture click here
June 5, Tuesday: Unconstrained Optimal Control, Kuhn-Tucker reformulation, Review
June 7, Thursday: Exam (the first 90 minutes),
The material for the Exam includes the material covered up to the Review.
There will be 7 questions on the
exam. You have to answer 3 questions
out
of questions 1-6, and you have to answer question 7. Each
question is
worth 25 points (100 points total). You may bring one page freely
written on
both sides.
Exam Median=? (???%) (xx
students).
Highest
mark for the exam: ?
June 14, Thursday: Varia
If you have any questions or remarks, send them to me
Spring 2007