Lecturer: Harri Ehtamo
Assistant: Anton von Schantz
- We organize an online exam, where you have a chance to get a numeric grade 1-5.
- The online exam is Thu 28.5 18:00 - Fri 29.5 16:00. You must register in Weboodi to attend.
- Those who register will receive the exam and instructions by email Thu 28.5 18:00.
- See Guide to self-study and preparation for how to study for the exam.
- The online exam is the same as a regular exam with 5 problems to solve (max 30 points, 6 points/problem).
- Your scaled points are added to the exam points. However, you still need 12 points in the exam to pass. The limits for the other grades are decided later.
Why this course?
This course examines dynamic (aka multistage) optimization models. They capture many relevant real-life problems: scheduling, route planning, solving optimal strategies for games, inventory control, investment problems, machine repair, text processing, dna sequence matching, stopping problems, airplane/rocket flight path optimization, minimum time/effort problems, optimal fishery management, saving/consumption optimization, optimal feedback controllers for plants and regulator problems and so on.
The models that are examined are
- Optimal control problem. Find control u(t) that makes the system trace
the optimal trajectory x*(t) that minimizes the cost .
Function a describes how the system behaves at state x(t) at time t under control u(t). The cost function J consists of start and end point costs and running cost that is given by function L that may depend on the state x(t) and control u(t).
- Calculus of variations. Find continuous/differentiable curve y(x) that is extremum for
- Dynamic Programming (DP) problem. Find optimal controls u_k (optimal policy) that minimizes the expected cost
of the discrete stochastic system
f_k describes how the system evolves to the next state x_k+1 when the state is x_k, control u_k is chosen and there is stochastic disturbance is w_k. The cost function is given by g_k. This is discrete version of the optimal control problem.
Teaching: Lectures (24h) and exercise sessions (24h)
Assessment methods: Exam, homework, attending exercises and lectures, and project work.
Grading scale: Pass or 0-5
Study material: Lecture slides and exercises. Additional reading:
- D. E. Kirk: Optimal Control Theory. Prentice Hall, 1970 (2004). (<- the main book)
- D. P. Bertsekas: Dynamic Programming and Optimal Control, vol 1(and 2). Athena Scientific, 1995
- M. L. Kamien and N. L. Schwartz: Dynamic Optimization - The calculus of variations and optimal control in economics and management, 2nd edition. North Holland, 1991.
Language of instruction: English
Prerequisites: 1st and 2nd years math, recommended MS-C2105 Optimoinnin perusteet (or equivalent)