Osion kuvaus

  • Completing the course

    In spring 2021, the course is 100% self-study. So there is no contact teaching/Zoom teaching. However, the course has a Slack discussion forum, where students can discuss topics and homework assignments of the course. See the Slack discussion forum page for more details.

    There are 2 homework assignments per exercise, 4 per week, altogether 20 homework assignments. These are based on the lecture material in question and the corresponding solved exercise problems. See Assignments for practical information about submitting, deadlines, and grading of homework assignments.

    Weekly Schedule

    The students can familiarize with the course topics in their own phase, but the teachers, lectures and exercises follow the following schedule:
    1. Introduction, calculus of variations, Euler equation (Week 2).
    2. Calculus of variations, transversality conditions (Week 2).
    3. Optimal control (Week 3).
    4. Pontryagin minimum principle, infinite time horizon in calculus of variations (Week 3).
    5. Minimum time and control-effort problems (Week 4).
    6. Dynamic Programming (DP), discrete time/state problems (Week 4).
    7. DP applications (Week 5).
    8. Continuous time problem, HJB equation (Week 6).
    9. Discounted problems, numerical methods (Week 6).

    Learning goals

    After the course, the student should have learned the following things:
    • Solving continuous time problems using calculus of variations, including different end point conditions. Lectures 1-2 (Kirk Section 4).
    • Solving optimal control problems, including different end point conditions, and minimum principle. Lectures 3-5 (Kirk Section 5).
    • Solving infinite horizon problems. Lecture 4 (Bertsekas Vol 2, Section 1).
    • Solving discrete time/state problems using DP algorithm, including stochastic problems. Lectures 6-7 (Bertsekas Vol 1, Sections 1-5).
    • Solve continuous time problems using Hamilton-Jacobi-Bellman equation. Lecture 8 (Kirk Section 3.11).
    • Discounted problems and numerical methods, e.g. value- and policy iterations. Lecture 9 (Bertsekas Vol 1 Section 7).
    • Learning definitions for relevant concepts and terminology used in the course. These definitions are often asked in course exams.


    See Online exam for practical details about the exam.


    30 points from exam + a maximum of 12 extra points. A maximum of 12 extra points can be obtained from homework (12 points) and activity on Slack discussion forum (6 points). For example,  6 points from homework and 6 from activity, or 12 points from homework, and 0 from activity, and so on.

    Grade/lower grade limit in points:

    5/27; 4/24; 3/21; 2/18; 1/12 

    The extra points do not help in passing the course. To pass the course one must get at least 12 points in the exam.