ECE 6710 Optimal Control Systems
Fall 2020
version 9 December 2020
Instructor
Dr. Damon
A. Miller, Associate Professor of Electrical and Computer Engineering, Western
Michigan University, College of Engineering and Applied Sciences, Floyd Hall,
Room A-240, 269.276.3158, 269.276.3151 (fax), damon.miller@wmich.edu, www.homepages.wmich.edu/~miller/.
Course Format Summary
Lectures will be
conducted synchronous online at the scheduled class meeting time.
Office Hours
Dr. Miller is
available for online office hours W 4:00PM-5:00PM at https://wmich.webex.com/meet/damon.miller.
Note that you may be online with other students; discussions related to
confidential issues are by appointment as requested by email to damon.miller@wmich.edu.
Catalog Description
ECE 6710 Optimal
Control Systems (3-0), 3 hrs. Optimal
control dynamic programming, Portryagin’s principle, linear optimal regulator,
system identification. Stochastic and adaptive control. Prerequisite: ECE 6700
Modern Control Theory.
Acknowledgements
Dr. Miller thanks Dr.
Raghe Gejji for his support in preparing course materials. He also thanks the
Educational Technology Department for contributions to this syllabus.
Adapted/adopted in part from syllabi by J. Gesink and J. Kelemen.
Copyright
Information
Materials prepared by
Dr. Miller are © 2020 Damon A. Miller. Other copyrights apply to materials such
as text and images from books, datasheets, etc. Consult source documents for
copyright information.
Due to the unusual
circumstances, I am providing my handwritten lecture notes for your personal use
in ECE 6710 only. These must never be distributed or posted in any way. Since
the notes are meant only as a supplement to the text, they may contain verbatim
material from the text without quotes. The notes must not be considered as a
primary source and never referenced. The text is the primary source, unless
otherwise noted.
Textbook
and Materials
Required:
1.
You
must have access to a computer less
than 5-years old with a webcam and microphone and high-speed internet access. This is required for
online lectures and Dr. Miller’s office hours.
2.
Text: F. L. Lewis, D. L. Vrable, V. L.
Symore, Optimal Control, John Wiley
& Sons, Inc, 3rd edition, 2012.
3.
The MathWorks, MATLAB®, any reasonably recent version will suffice. The CAE center provides access to this
software; however, students are strongly encouraged to have access on their
personal computer*.
*You may
use a different programming language at your own risk if they include access to
comparable optimization routines.
References
(also see course schedule):
1.
T.
W. Colthurst (founding editor) et al., “The Hessian,” World Web Math, available here.
2.
M.
J. Maron, Numerical Analysis: A Practical
Approach, Macmillan, New York, 1982.
3.
J.
Wilde et al., Unconstrained Optimization,
available here.
4.
J.
Belk, Some Linear Algebra, available here.
5.
A.
Ali Ahmadi, review of linear algebra and multivariable calculus, available here.
6.
D.
Khoshnevisan, Some Linear Algebra,
available here.
7.
A.
Christian, Definiteness of Quadratic
Forms, available here.
8.
S.
Webb, T. Croft, L. Mustoe, J. Ward, z-Transforms
and Difference Equations, part of Engineering Mathematics Open Learning
Project, available here.
9.
G.
L. Plett, ECE4520/5520: Multivariable
Control Systems I Lecture Notes: CH 6, available here.
10.
M.
de Oliveria, Solution to Linear
Time-Invariant Systems, available here.
11. Weisstein, Eric W. "Leibniz Integral Rule." From MathWorld--A
Wolfram Web Resource. https://mathworld.wolfram.com/LeibnizIntegralRule.html
12. P. Haile, Differentiating
an Integral, available at http://www.econ.yale.edu/~pah29/409web/leibniz.pdf
13.
G.
B. Thomas, Jr. and R. L. Finney, Calculus
and Analytical Geometry, 5th ed., Addison-Wesley, 1982.
14.
Wolfram
Language & System Documentation Center, Numerical
Solution of Boundary Value Problems (BVP), available at https://reference.wolfram.com/language/tutorial/NDSolveBVP.html
15.
L.
F. Shampine, J. Kierzenka, and M. W. Reichelt, Solving Boundary Value Problems for Ordinary Di erential Equations in
MATLAB with bvp4c, available at https://classes.engineering.wustl.edu/che512/bvp_paper.pdf
16.
K.
B. Petersen and M. S. Pederson, The
Matrix Cookbook, available at https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
Course
Policies
Academic Honesty
General:
Students are responsible for making
themselves aware of and understanding the University policies and procedures
that pertain to Academic Honesty. These policies include cheating, fabrication,
falsification and forgery, multiple submission, plagiarism, complicity and
computer misuse. The academic policies addressing Student Rights and
Responsibilities can be found in the Undergraduate Catalog at http://catalog.wmich.edu/index.php?catoid=32 and the Graduate
Catalog at http://catalog.wmich.edu/index.php?catoid=33. If there is
reason to believe you have been involved in academic dishonesty, you will be
referred to the Office of Student Conduct. You will be given the opportunity to
review the charge(s) and if you believe you are not responsible, you will have
the opportunity for a hearing. You should consult with your instructor if you
are uncertain about an issue of academic honesty prior to the submission of an
assignment or test.
Students and instructors are responsible
for making themselves aware of and abiding by the “Western Michigan University
Sexual and Gender-Based Harassment and Violence, Intimate Partner Violence, and
Stalking Policy and Procedures” related to prohibited sexual misconduct under
Title IX, the Clery Act and the Violence Against Women Act (VAWA) and Campus
Safe. Under this policy, responsible employees (including instructors) are
required to report claims of sexual misconduct to the Title IX Coordinator or
designee (located in the Office of Institutional Equity). Responsible employees
are not confidential resources. For a complete list of resources and
more information about the policy see http://www.wmich.edu/sexualmisconduct.
In addition, students are encouraged to
access the Code of Conduct, as well as resources and general academic policies
on such issues as diversity, religious observance, and student disabilities:
·
Office
of Student Conduct http://www.wmich.edu/conduct
·
Division
of Student Affairs http://www.wmich.edu/students/diversity
·
Registrar’s
Office http://www.wmich.edu/registrar/calendars/interfaith
·
Disability
Services for Students http://www.wmich.edu/disabilityservices.
—
section provided by the WMU Faculty Senate with minor link reformatting
Plagiarism:
For
an in-depth exploration of plagiarism, see http://libguides.wmich.edu/plagiarism
COVID-19 Statement
Due to the current
COVID-19 Pandemic, and consistent with the State of Michigan* requirements and
the WMU Safe Return plan (https://wmich.edu/safereturn), safety requirements are in place to minimize exposure to the
Western Michigan University community. These guidelines apply to all in-person
or hybrid classes held either inside or outside a WMU building.
Facial coverings
(masks), over both the nose and mouth, are required for all students
while in class, no matter the size of the space. This includes outdoor class
settings where social distancing is not possible (i.e., at least six feet of
space between individuals). Following this recommendation can minimize the
transmission of the virus, which is spread between people interacting in close
proximity through speaking, coughing, or sneezing. During specified classes in
which facial coverings (masks) would prevent required class elements, students
may remove facial coverings (masks) with instructor permission, in accordance
with the exceptions in the Facial Covering (mask) Policy** ("such as playing an instrument, acting, singing, etc.").
Facial coverings (masks)
must remain in place throughout the class. Any student who removes the
mandatory facial covering (mask) during class will be required to leave the
classroom immediately.
Facial coverings (masks)
are not a substitute for social distancing. Students shall observe current
social distancing guidelines in all instructional spaces, both indoors and
outdoors. Students should avoid congregating around instructional space
entrances before and after class sessions. Students should exit the
instructional space immediately after the end of class to help ensure social
distancing and to allow for those attending the next scheduled class session to
enter.
Students who are unable
to wear a facial covering (mask) for medical reasons must contact Disability
Services for Students (https://wmich.edu/disabilityservices) before they attend class.
These guidelines are in
place to ensure the safety of all students, faculty, and staff during the
pandemic. Noncompliance is a violation of the class requirements and the
Student Code of Honor (https:/wmich.edu/conduct/expectations-students).
*For current State of
Michigan Executive orders, see:
https://www.michigan.gov/whitmer/0,9309,7-387-90499_90705---,00.html
**For the WMU Facial
Covering (Mask) Policy, see:
https://wmich.edu/policies/facial-covering-mask
—
statement provided by the WMU Faculty Senate
Accommodations
If you have a
documented disability and verification from the Disability Services for
Students (DSS), and wish to discuss academic accommodations, please contact
your instructor as soon as possible. It is the student’s responsibility to
provide documentation of disability to DSS and meet with a DSS counselor to
request special accommodation before classes start.
Grading Basis
Projects
(100%) will be assigned on a regular basis.
LATE PROJECTS WILL NOT BE
ACCEPTED AND ARE DUE AS INDICATED VIA ELEARNING DROPBOX. All projects are
to be completed individually. Projects
may include/consist of a series of homework style problems. Use the prescribed
homework format for those problems. Be sure to follow the guidelines for computer
assignments.
OUTSTANDING
WORK might earn extra credit. The first student to report an error in any material
prepared by the instructor(s) will earn extra credit. The course grading scale
is:
Scale:
0-59 E | 60-64 D | 65-69 DC | 70-74 C | 75-79 CB | 80-84 B | 85-89 BA | 90-100
A |
Numeric scores are rounded to the nearest integer.
Midterm
grades are not assigned.
Grade
Appeals
If you have a
question regarding a graded assignment, contact Dr. Miller within TWO business days of receiving the
grade for the assignment in question.
Late
Assignments will
not be accepted without a documented excuse. If an emergency prevents you from
submitting an assignment on-time, contact your instructor PRIOR to the
assignment due date or as soon as you can, via email. Failure to adhere to this policy will result
in zero credit for the assignment.
HOMEWORK contributes to the project grade
category. Each homework problem must be worked on separate page(s). LATE HOMEWORK will not be accepted, except
under extraordinary circumstances. Homework
is to be completed individually.
Homework should normally be done on
8 1/2'' by 11'' sheets and scanned for submission. “Engineer's Pad” sheets are
preferred. Solutions must be done in a
neat, structured, logical, and orderly manner with frequent brief notations
enabling the grader to readily verify the author's source of information, steps
taken, sources of formulas, equations, and methods used. USE THE PARTIAL CHECK LIST FOR SUBMITTED HOMEWORK BELOW. Papers failing to meet these guidelines may
not be graded and may be returned, with or without an opportunity for
resubmission with a penalty.
PARTIAL
CHECK LIST FOR SUBMITTED HOMEWORK
COMPUTER
ASSIGNMENTS must
be implemented via MATLAB®.
Computer assignments must include
1.
a
problem statement;
2.
description
of techniques utilized including pseudo-code (as in “listings” in the text);
3.
results;
4.
discussion
of results; and
5.
computer
code listing(s) attached as an appendix. Computer code must include explanatory
comments. Some of those comments should relate computer code to the pseudo-code
of item 2 above. Use modular
programming.
Project Submission
Submit your files as a compressed folder (.zip format)
attachment to your instructor’s Elearning Dropbox by the indicated due date.
The folder must contain ONLY the report in pdf format. No other files will be
considered. The folder must be named in this format: “LastNameFirstName_Project#”;
for example, “DoeJane_Project1” is Jane Doe’s Project 1 submission.
Submissions deviating from these
instructions will not be accepted.
Course
Schedule
The schedule will
be frequently updated as the semester progresses.
|
# |
date |
topic |
assignments |
|
WEEK
1 |
|||
|
|
9/2 |
ONLINE LECTURE NOT
AVAILABLE DUE TO INFRASTRUCTURE ISSUE |
Read CH 1 |
WEEK
2 |
|||
|
1 |
9/9 |
1.
Static Optimization (CH 1) SYNCHRONOUS ONLINE
LECTURE AT 4PM |
Read CH 2.1 Project 1 (CH 1)
DUE by 9/16 5PM 1.
TEXT
PROBLEM 1-1.1 2.
TEXT
PROBLEM 1.1-2 Also:
use MATLAB® to numerically find the minimum using: fminsearch(); compare
results. 3.
TEXT
PROBLEM 1.1-3 4.
TEXT
PROBLEM 1.2-1 5.
TEXT
PROBLEM 1.2-5. 6.
TEXT
PROBLEM 1.2-7 7.
EXAMPLE
1.2-2. Select values for Q, R, B,
c for m=n=2. Find the optimal control u
by hand. Then use the algorithm of 1.3
Numerical Solution Methods to find u.
Also find u using MATLAB fmincon().
Compare the three results. 8.
Apply
what you learned in CH 1 to minimization of the Rosenbrock function [ref] |
|
WEEK
3 |
|||
|
2 |
9/16 |
2.
Solution of the General
Discrete-Time Optimization Problem
(CH 2.1) |
Read CH 2.2 Submit to ELearning
Dropbox 1.
Duplicate
the results of the computer simulations on page 30 of the text (fixed and
free final state). 2.
TEXT
PROBLEM 2.1-1 3.
Complete
TEXT PROBLEM 2.1-2
|
|
WEEK
4 |
|||
|
|
9/23 |
NO
CLASS: TECHNICAL DIFFICULTIES |
|
|
WEEK
5 |
|||
|
3 |
9/30 |
3.
Discrete-Time Linear-Quadratic
Regulator (CH
2.2) |
Read CH 2.3 and CH
2.4 Project 3 (CH 2.2)
DUE BY10/7 by 5PM. Submit to ELearning Dropbox 1.
See
if you can show that the coefficient matrix of (2.2-9) is Hamiltonian. I
could not L. 2.
TEXT
PROBLEM 2.2-4. 3.
TEXT
PROBLEM 2.2-5. 4.
TEXT
PROBLEM 2.2-8(a). 5.
TEXT
PROBLEM 2.2-9 |
|
WEEK
6 |
|||
|
4 |
10/7 |
4.
Digital Control of Continuous
Time Systems (CH
2.3) 5.
Steady-State Closed-Loop Control
and Suboptimal Feedback
(CH 2.4) |
Read CH 3.1-3.3 Project 4 (CH 2.3
and CH 2.4) 1.
Duplicate
the results of Example 2.3-1 2.
TEXT
PROBLEM 2.3-2 3.
Duplicate
the results of Example 2.3-2 and 2.4-1. Verify that the suboptimal cost Jk
is greater than the optimal cost J*k for all k. 4.
Duplicate
results of Example 2.4-3 via simulation. 5.
Duplicate
results of Example 2.4-4. 6.
Duplicate
results of Example 2.4-6. 7.
TEXT
PROBLEM 2.4-2 |
|
WEEK
7 |
|||
|
5 |
10/14 |
Steady-State
Closed-Loop Control and Suboptimal Feedback (CH 2.4) |
|
|
WEEK
8 |
|||
|
6 |
10/21 |
6.
The Calculus of Variations (CH 3.1) 7.
Solution of the General
Continuous-Time Optimization Problem (CH 3.2) |
Project 5 (CH 3.2) 1.
TEXT
PROBLEM 3.2-1 2.
TEXT
PROBLEM 3.2-2; simulate your solution and plot lambda*, u*, x*, and J as a
function of time. 3.
EXTRA
CREDIT: Improve Dr. Miller’s derivation of Table 3.2-1 4.
EXTRA
CREDIT: Derive 3.2-11 |
|
WEEK
9 |
|||
|
7 |
10.28 |
8.
Q/A
Session |
|
|
WEEK
10 |
|||
|
8 |
11/4 |
Solution of the General
Continuous-Time Optimization Problem (CH 3.2) 9.
Solution of Two-point
Boundary-value Problems
(CH 3.2 subsection) 10.
Continuous-Time Linear Quadratic
Regulator (CH
3.3) |
Read CH 4.1 1.
TEXT
PROBLEM 3.2-8 2.
TEXT
PROBLEM 3.3-1 3.
TEXT
PROBLEM 3.3-3 |
|
WEEK
11 |
|||
|
9 |
11/11 |
11.
The Tracking Problem (CH 4.1) 12.
Regulator with Function of Final
State Fixed (CH 4.2) |
Read 5.2 Project 7 (CH 4.1
and 4.2) 1.
TEXT
PROBLEM 4.1-3.
|
|
WEEK
12 |
|||
|
10 |
11/18 |
13.
Constrained Input Problems w/ Bang-Bang Control |
Read CH 6.1-6.2 Project 8 (CH 5.2) 1.
TEXT
PROBLEM 5.2-2 |
|
N/A |
|||
|
|
11/25 |
Thanksgiving
break |
|
|
WEEK
13 |
|||
|
11 |
12/2 |
14.
Review
Project 1 |
|
|
WEEK
14 |
|
||
|
12 |
12/9 |
15.
Bellman’s Principle of Optimality
(CH 6.1) 16.
Discrete-Time Systems (Ch 6.2) |
Project 9 (CH 6) 1.
Example
6.1-2, pg. 263 2.
Example
6.1-3, pg. 263 3.
Example
6.1-4(a), pg. 263 4.
Text
Problem 6.2-1 DUE 12/16 BY 7PM |
|
|
12/11 |
LAST DAY TO WITHDRAW (extended) |
|
|
WEEK
15 |
|||
|
13 |
12/16 Wed |
Final
Exam: 5-7PM |
|
|
|
|
||