EML 6364 - Optimal Control
Spring 2026
COURSE INSTRUCTOR
Name: Dr. Anil V. Rao
Office: MAE-A 314
E-mail: anilvrao@ufl.edu
Tel: 352-392-5523 (Office); (352) 672-1529 (Mobile).
YouTube Channel: https://www.youtube.com/user/anilvrao2
Teaching Assistant: Emily Palmer
Contact: Via Canvas
All contact methods are acceptable! Note for fastest response it is best to reach me on my mobile phone.
Office: MAE-A 314
E-mail: anilvrao@ufl.edu
Tel: 352-392-5523 (Office); (352) 672-1529 (Mobile).
YouTube Channel: https://www.youtube.com/user/anilvrao2
Teaching Assistant: Emily Palmer
Contact: Via Canvas
All contact methods are acceptable! Note for fastest response it is best to reach me on my mobile phone.
COURSE LOCATIONS AND CLASS PERIODS
Class Period: Tuesday 3:00 PM to 4:55 PM (Periods 8 and 9); Thursday 4:05 PM to 4:55 PM (Period 9). Attendance is expected.
Lecture Room: NEB 100
Online Videos: Class will be recorded via UF EDGE
Office Hours: MW 3:00 PM to 5:00 PM (As Needed — In Person). Evenings: Wed 7:00 PM to 8:00 PM (As Needed — Zoom)
Office Hours Zoom Link:
• Meeting ID: 923 2838 8258
• Click here for Zoom link or copy and paste the following URL into your browser: https://ufl.zoom.us/j/92328388258.
Lecture Room: NEB 100
Online Videos: Class will be recorded via UF EDGE
Office Hours: MW 3:00 PM to 5:00 PM (As Needed — In Person). Evenings: Wed 7:00 PM to 8:00 PM (As Needed — Zoom)
Office Hours Zoom Link:
• Meeting ID: 923 2838 8258
• Click here for Zoom link or copy and paste the following URL into your browser: https://ufl.zoom.us/j/92328388258.
CATALOG DESCRIPTION
Calculus of variations, calculus of variations applied to optimal control, nonlinear optimization, numerical Methods for optimal control
PREREQUISITES
Differential and integral calculus, ordinary and partial differential equations
COURSE OBJECTIVES
• Develop the fundamentals of calculus of variations
• Develop fundamentals of optimal control theory using calculus of variations
• Introduce major numerical methods for solving constrained optimal control problems
• Develop fundamentals of optimal control theory using calculus of variations
• Introduce major numerical methods for solving constrained optimal control problems
IMPORTANT NOTE
I consider it an honor and a privilege to be able to teach all of you, and I intend to provide the best instruction possible in order to enable you to learn the material well. If you cannot make office hours, please contact me and we will set up a time for you to get help. Regardless of how busy I am with other things, I will do what I am able to make myself available.
APPROXIMATE SCHEDULE FOR MATERIAL
Topic
Review of Minima and Maxima of Functions
Calculus of Variations
Calculus of Variations
Applied to
Optimal Control Problems
Nonlinear Optimization
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Numerical Methods for Optimal Control
Material Covered
Optimization of Function of One Variable
Develop Theory of Calculus of Variations
Optimality Conditions, Linear Quadratic Control, Pontryagin's
Minimum Principle, Bang — Bang Optimal Control,
Singular Arcs
Unconstrained and Constrained
Finite-Dimensional Optimization
Indirect Methods and Direct Methods
Schedule
Week 1
Weeks 2 and 3
Weeks 4 through 8
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Week 9
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Week 10 through 13
OFFICE HOURS
Anil Rao (instructor): Monday and Wednesday 3:00 PM to 5:00 PM
Location: Reitz Union Food Court
Emily Palmer (Teaching Assistant): TBD
Location: Zoom
Note: if for some reason you are unable to make my office hours, you can always schedule an appointment at a time that is mutually agreeable to both you and I.
Location: Reitz Union Food Court
Emily Palmer (Teaching Assistant): TBD
Location: Zoom
Note: if for some reason you are unable to make my office hours, you can always schedule an appointment at a time that is mutually agreeable to both you and I.
OFFICE HOURS
Name
Anil V. Rao
(Instructor)
Times
MWF
3:00 PM to 4:00 PM
Meeting Location and Contact
Zoom: https://ufl.zoom.us/j/92338141900
(Meeting ID: 923 3814 1900)
anilvrao@ufl.edu
PERSONAL HOURS
I have found that often students want to talk with me about topics other than the course. Sometimes it is just to get career directions and advice, other times to find out about opportunities to work in my research group as an undergraduate or graduate student. Because students would like to have conversations on such topics (and other topics), each week I will hold what I call "personal hours". If you are interested in just having a conversation with me that is not specific to the course material, please join me for personal hours. I will try to make these hours actual in person hours because I feel it is the best way to have non-technical conversations. As a result, I will hold personal hours in the Reitz Union food court.
Personal Office Hours Times
Friday
4:00 PM to 5:00 PM
Meeting Location
Reitz Union Food Court
(Next to Starbucks)
Note: I am happy to schedule other times for personal meetings about topics not related to the course. Please feel free to ask.
TEXTBOOK
Kirk, D. E., Optimal Control Theory: An Introduction, Dover Publications, 1970.
HOMEWORK ASSIGNMENTS
The assignments for this class are posted on the Canvas site for the course on E-Learning. Below is a list of these assignments.
Assignment
Assignment #1
Assignment #2
Assignment #3
COURSE PROJECT
One of the key assignments in this class is a course project. The project can be found by clicking here. The instructions are as follows. Choose two optimal control problems, one from the "elementary" pptimal control problems list and one from the "advanced" optimal control problems list. For the problem you choose from "elementary" list you must formulate the complete set of first-order optimality conditions for your problem using the calculus of variations. You must then solve your problem using an indirect numerical method and a direct numerical method that we have studied in the course. Next, for the problem you choose from "advanced" list you must choose a single method (indirect or direct but not both). You must then analyze the quality of your solution. In your analysis, consider the following questions. Can you determine the proximity of your numerical solution to the “true” optimal solution. If you are unable to ascertain how close your solution is to the true optimal, how do you know you have obtained a reasonable approximation? What is the computational efficiency of the methods you applied to solve your problem? What are the limitations of the methods you have chosen on your problem. Given your analysis, what numerical method would you seek in order to overcome the deficiencies you found with the methods you chose? It is highly recommended that you now wait until the last minute to think of a problem for your project! The course project is due on the last day of class. Click here to download a copy of the course project.
ATTENDANCE RULES
Regular attendance is expected of all students.
CHEATING
Cheating of any kind in this course will be enforced in accordance with the university rules. Any violation of any kind (even something as simple as a single line of code that is identical in the homework of two students) will automatically result in an "E" in the course and will reported as appropriate to the Dean of Students Office.
MAKE-UP POLICY
Because all assignments in this course are not time limited (in the same manner as that a usual in-class exam), make-ups will be provided on a case-by-case basis. If you have an issue (illness, other urgent matter), please discuss it with me and we will work to find a fair and reasonable solution.
COURSE GRADING
Item
Homework Assignments
Midterm Exam
Project
Total
Point Value
30
30
40
100 Points
GRADING SCALE
Grades in this course are determined using the following scale:
Letter Grade
A
A-
B+
B
B-
C+
C
C-
D+
D
D-
E
Score Range
95 and Above
90 to less than 95
85 to less than 90
80 to less than 85
75 to less than 80
70 to less than 75
65 to less than 70
60 to less than 65
55 to less than 60
50 to less than 55
45 to less than 50
Less Than 45
NOTES ON ASSIGNMENT OF FINAL LETTER GRADES
• The grading scale posted above is not flexible.
• Any score on the boundary between two ranges will receive the higher grade (for example, a 94 receives a grade of "A-").
• Finally, it is noted that while your individual scores for assignments, exams, and quizzes will be posted on E-learning (Canvas), the Canvas portal may not accurately reflect a student's relative standing in the class. Regardless of the information that is seen in Canvas, computation of final grades will be based on the criteria set forth above and a student's grade will only be final when grades have been computed at the end of the semester.
IMPORTANT NOTE: Any assignment either not submitted or not completed with a good faith effort (where the judgment of "good faith effort" rests wholly with me) will result in a full letter grade deduction in the course. For example, if the final score falls into the category of an "A-" and one homework or quiz is not submitted or is deemed to not have been performed with a good faith effort, the final grade will be a "B-". This policy is not flexible.
• Any score on the boundary between two ranges will receive the higher grade (for example, a 94 receives a grade of "A-").
• Finally, it is noted that while your individual scores for assignments, exams, and quizzes will be posted on E-learning (Canvas), the Canvas portal may not accurately reflect a student's relative standing in the class. Regardless of the information that is seen in Canvas, computation of final grades will be based on the criteria set forth above and a student's grade will only be final when grades have been computed at the end of the semester.
IMPORTANT NOTE: Any assignment either not submitted or not completed with a good faith effort (where the judgment of "good faith effort" rests wholly with me) will result in a full letter grade deduction in the course. For example, if the final score falls into the category of an "A-" and one homework or quiz is not submitted or is deemed to not have been performed with a good faith effort, the final grade will be a "B-". This policy is not flexible.
ACADEMIC POLICIES AND RESOURCES
To support consistent and accessible communication of university-wide student resources, instructors must include this link to academic policies and campus resources: https://go.ufl.edu/syllabuspolicies. Instructor-specific guidelines for courses must accommodate these policies.
COMMITMENT TO A POSITIVE LEARNING ENVIRONMENT
The Herbert Wertheim College of Engineering values varied perspectives and lived experiences within our community and is committed to supporting the University’s core values.
If you feel like your performance in class is being impacted by discrimination or harassment of any kind, please contact your instructor or any of the following:
• Your academic advisor or Graduate Coordinator
• HWCOE Human Resources, 352-392-0904, student-support-hr@eng.ufl.edu
• Pam Dickrell, Associate Dean of Student Affairs, 352-392-2177, pld@ufl.edu
If you feel like your performance in class is being impacted by discrimination or harassment of any kind, please contact your instructor or any of the following:
• Your academic advisor or Graduate Coordinator
• HWCOE Human Resources, 352-392-0904, student-support-hr@eng.ufl.edu
• Pam Dickrell, Associate Dean of Student Affairs, 352-392-2177, pld@ufl.edu
