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TSRT08 Optimal control

Optimal control consists of theory and methods for controlling dynamical systems so that a mathematical criterion is minimized. The course aims at giving basic theory and engineering oriented computational methods in the area. After taking the course the participants are expected to be able to:

  • Analyze and synthesize optimal open loop control signals using the Maximum principle.

  • Analyze and synthesize optimal feedback laws using the Hamilton-Jacobi-Bellman equation.

  • Use numerical software to solve optimal control problems.

  • Describe the connections between optimal control and other optimization approaches.


The course consists of


Exam and three homework assignments.

Lecturer and course responsible

Lectures are held by

Examinator Anders Hansson, tel: 013 281681.

Teaching Assistant

Exercise sessions are held by
Lektionsledare Daniel Arnström, tel: 076 8312409.


The schedule for the course can be found here.


  • Optimal Control - Lecture notes by Ulf Jönsson in collaboration with Claes Trygger and Petter Ögren, Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden.
  • Optimal Control, TSRT08: Exercises - Exercises with solutions. Can also be downloaded here.
  • Formula sheet that is going to be used at the examination.
  • MPC tutorial can be useful for the second homework assignment.
  • A manual for the MPT toolbox can be found here.

The lecture notes and the exercises can be bought at Bokakademin. Other material can be printed from this homepage.

Computer Software

The following software will be used during the course:

  • Matlab, tool for technical computing that should be well-known to the course participants.

  • PROPT, a Matlab toolbox for solving optimal control problems. PROPT manual with many examples.

Informationsansvarig: Daniel Arnström
Senast uppdaterad: 2022-03-17