# Optimal Control

**PhD Course on Optimal Control**

**Lecturers: **Kaoru Yamamoto (course responsible), Yury Orlov

**News: **

- The date of project presentation has changed to Apr 5 (Thu), 13:15 - 15:00.
- The date of exercise 6 has changed to Mar 1 (Thu). The room is
**Konferensrum stort****, 1172 (lab F****).** - Jan 30 - Typo corrected in the lecture slides of L2.
- Jan 23 - Typo corrected in the lecture slides of L1.

** **

**Couse Description: **This course introduces calculus of variations and optimal control theory. The course covers key topics in optimal control such as the maximum principle, dynamic programming and the Hamilton-Jacobi-Bellman equation, and the linear-quadratic regulator.

**Location and Time: **With a few exceptions, all lectures and exercise sessions are given in the

**seminar room (M:2112B)**at

**13:15-15:00**on Tuesdays and Thursdays.

**Lectures:**

- Jan 23 (Tue): L1 Functional minimization, Calculus of variations (CV) problem
- Jan 30 (Tue): L2 Constrained CV problems, From CV to optimal control
- Feb 6 (Tue): L3 Maximum principle, Existance of optimal control
- Feb 13 (Tue): L4 Maximum principle (proof)
- Feb 20 (Tue): L5 Dynamic programming, Hamilton-Jacobi-Bellman equation
- Feb 27 (Tue): L6 Linear quadratic regulator
- Mar 5 (
**Mon**): L7 Numerical methods for optimal control problems **Apr 5 (Thu)**: L8 Student presentations

**Exercises:**

- Jan 26 (
**Fri**): E1 - Feb 1 (Thu): E2
- Feb 8 (Thu): E3
- Feb 15 (Thu): E4
- Feb 22 (Thu): E5
- Mar 1 (Thu): E6
**at lab F**

**Readings: **Daniel Liberzon, Calculus of Variations and Optimal Control: A Concise Introduction, Princeton University Press, 2012. ISBN 978-0-691-15187-8.