Spring 2025
MTH 496 Capstone in Mathematics
- Course website - D2L
-
Lecture: LEC3
- Instructor: Son Tu – tuson@msu.edu
- Wells Hall A222 (MWF: 11:30 am - 12:20 pm).
-
Grader: Ming-Wei Kuo - kuomingw@msu.edu
Please email Ming-Wei Kuo regarding grading questions and cc me in the email. Thank you! -
Office hours:
- Time: Monday from 1:00pm – 2:00pm, Friday 1:00 - 2:00 pm, and by appointment.
- Piazza Signup Link: https://piazza.com/msu/spring2025/ba32
- Syllabus: pdf
- Schedule: pdf
- How to reach me? You can reach me by sending an email to tuson@msu.edu. All emails will be answered within 24 hours (most likely within 10 hours).
- Getting help:
Materials
- All materials are hosted on D2L.
- Some lecture notes are posted here for convenience: MSU - Google Drive
-
Some extra readings:
-
(2025-03-16) 300 Years Of Optimal Control: From The Brachystochrone to the Maximum Principle – Google Drive – DOI
The Brachistochrone Problem and Modern Control Theory
Authors: H.J. Sussmann; J.C. Willems. - Brachistochrone Optimal Control, Python
- Calculus of Variations
- Legendre–Clebsch condition
-
(2025-03-16) 300 Years Of Optimal Control: From The Brachystochrone to the Maximum Principle – Google Drive – DOI
| Date | No. | Description | File |
|---|---|---|---|
| 2025-01-13 | 01 | Introduction to Optimal Control Theory | Lecture 01 | 2025-01-15 | 02 | Geometric solutions to the Rocket Railroad Car problem, Introduction to ODEs | Lecture 02 | 2025-01-17 | 03 | Review on Linear ODEs | Lecture 03 | 2025-01-22 | 04 | Review on Linear ODEs, Gronwall's inequality | Lecture 04 | 2025-01-24 | 05 | Uniqueness and Picard's iteration, Picard-Linderlof's Theorem | Lecture 05 |
| Homework 01 is out | Homework 01 | 2025-01-27 | 06 | Examples of Picard's iteration | Lecture 06 | 2025-01-29 | 07 | Numerical Implementations (Picard's Iteration and Forward Euler Method) | Lecture 07, Codes | 2025-01-31 | 08 | The formulation of the Bolza problem | Lecture 08 | 2025-02-03 | 09 | Derivation of the Necessary Conditions, part 1 | Lecture 09 | 2025-02-05 | 10 | Derivation of the Necessary Conditions, part 2 | Lecture 10 | 2025-02-07 | 11 | Examples of Necessary Conditions | Lecture 11 |
| Homework 01 due | Homework 01 due | 2025-02-10 | 12 | Problem with unbounded controls, interpretation of the adjoint | Lecture 12 | 2025-02-12 | 13 | Principle of Optimality | Lecture 13 | 2025-02-14 | 14 | The Bolza problem | Lecture 14 |
| Homework 02 is out | Homework 02 | 2025-02-17 | 15 | More examples on The Bolza problem | Lecture 15 | 2025-02-19 | 16 | Minimal surface of revolution, Introduction to numerical method | Lecture 16 | 2025-02-21 | 17 | Problems with bounded controls | Lecture 17 | 2025-02-24 | 18 | Optimal control with multiple variables | Lecture 18 | 2025-02-26 | 19 | Optimal control with multiple variables - Linear Dynamics with Quadratic Costs | Lecture 19 | 2025-02-28 | 20 | Optimal control with multiple variables - Isoperimetric Constraints | Lecture 20 |
| Homework 02 due | Homework 02 due | ||
| 2025-03-02 | Spring Break | ||
| 2025-03-04 | Spring Break | ||
| 2025-03-06 | Spring Break | 2025-03-10 | 21 | Bang-Bang Control | Lecture 21 | 2025-03-12 | 22 | Bang-Bang Control and Singular Control | Lecture 22 | 2025-03-14 | 23 | Time optimal problem | Lecture 23 |
| Homework 03 is out | Homework 03 | ||
| 2025-03-17 | Midterm Exam | Midterm Exam | 2025-03-19 | 24 | Application: Rocket Railroad Car problem | Lecture 24 | 2025-03-21 | 25 | Application: the Brachistochrone problem | Lecture 25 | 2025-03-24 | 26 | Lecture 26 | 2025-03-26 | 27 | Lecture 27 | 2025-03-28 | 28 | Lecture 28 | 2025-03-31 | 29 | Lecture 29 | 2025-04-02 | 30 | Lecture 30 | 2025-04-04 | 31 | Lecture 31 | 2025-04-07 | 32 | Lecture 32 | 2025-04-09 | 33 | Lecture 33 | 2025-04-11 | 34 | Lecture 34 |
| Homework 04 is out | Homework 04 is out | 2025-04-14 | 35 | Lecture 35 | 2025-04-16 | 36 | Lecture 36 | 2025-04-18 | 37 | Lecture 37 | 2025-04-21 | 38 | Lecture 38 | 2025-04-23 | 39 | Lecture 39 |
| 2025-04-25 | Final Exam | Final Exam |
© 2016-2025 Son N. T. Tu. Powered by Ark. Last updated: November 02, 2025.