EP30.FSF1102 — Optimal Control Theory
Course description
This course introduces dynamic optimization with applications in economics and quantitative modeling. The course has two parts:
- Discrete Dynamic Programming using value functions, Bellman equations, backward induction, and infinite-horizon discounted optimization.
- Optimal Control Theory including calculus of variations, Euler–Lagrange equations, Pontryagin Maximum Principle (PMP), and the Hamilton–Jacobi–Bellman (HJB) framework.
Main topics include:
- Finite-horizon dynamic programming
- Infinite-horizon discounted dynamic programming
- Contraction mapping and existence of solutions
- Economic applications of DP
- Calculus of variations
- Euler–Lagrange equations
- Pontryagin Maximum Principle
- HJB equation
- Continuous-time economic models
Course requirements
Requirements for taking final /terminal exams
Students are allowed to take the final exam if their attendance score reaches 5 points or more (on the scale of 10).
Requirements for attending classes
Students are responsible for attending all classes. In case of absence from school due to force majeure reasons, sufficient and reasonable proofs must be provided. For each absence, 1 point will be deducted 1 point. Students who miss any classes more than 3 times, with or without reason, will be considered as failing to complete the course and have to re-register.
Students will be awarded points for constructive comments, these points are added to attendance points and group assignments.
Groups who do not submit the group work will receive a score of 0 (zero). Late submissions will be deducted for each day of late submission.
Requirements for in-class behaviour
The course is conducted on the principle of respecting learners and lecturers. Any behaviour that affects the teaching and learning process is strictly prohibited.
Students must come to class on time. Students who are late more than 10 minutes after class starts will not be allowed to attend the class. Do not make noise and affect others during the learning process.
Laptops and tablets are only used for the purpose of taking notes for and calculating for lectures and exercises, absolutely forbidden to use for other purposes.
Detailed content
The course content is organized into six chapters:
Chapter 1. Introduction to Dynamic Optimization
Chapter 2. Finite Horizon Problems
Chapter 3. Infinite Horizon Problem
Chapter 4. Introduction to optimal control
Chapter 5. Calculus of Variations
Chapter 6. Optimal Control
Lecturers
- Nguyen Van Quy
- Vuong Van Yen
- Duong Viet Thong
Teaching plan
Week 1
Week 3
Learning resources
- Dynamic Optimisation for Economists. TSE lecture note — Blanchet, A., 2025
- Calculus of Variations and Optimal Control Theory: A Concise Introduction — Liberzon, D., 2012
- Optimal Control — Draguna Vrabie, Frank L. Lewis, and Vassilis L. Syrmos, 2012
- Optimal Control Theory: Applications to Management Science and Economics — Suresh P. Sethi, 2020
- Lecture notes and slides