Course Syllabus for

# Optimal Control Optimal styrteori

## FRT105F, 7.5 credits

Valid from: Autumn 2023
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-03-12

## General Information

Division: Automatic Control
Course type: Third-cycle course
Teaching language: English

## Aim

Optimal control is the problem of determining the control function for a dynamical system to minimize a cost related to the system trajectory. The subject has its roots in the calculus of variations but it evolved to an independent branch of applied mathematics and engineering in the 1950s. The overall goal of the course is to provide an understanding of the main results in calculus of variations and optimal control, and how these results can be used in various applications such as in robotics, finance, economics, and biology

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• - understand Bellman principle of optimality,
• - understand the essential ideas of the Pontryagin Maximum Principle,
• - know the advantages and disadvantages of both dynamic programming and Pontryagin Maximum Principle.

Competences and Skills

For a passing grade the doctoral student must

• - learn how to derive the Bellman/HJB equation for optimal control problems using dynamic programming,
• - learn how to solve low dimensional optimal control problems using Pontryagin's Maximum Principle,
• - be able to implement numerical methods to solve optimal control problems.

## Course Contents

Dynamic programming. Pontryagin's maximum principle. Linear quadratic regulator. Numerical methods for optimal control problems.

## Course Literature

• Liberzon, D.: Calculus of variations and optimal control theory: a concise introduction. Princeton university press, 2011.
• Bertsekas, D.: Dynamic programming and optimal control: Volume I. Athena scientific, 2012.

Lecture notes written by lectures

## Instruction Details

Type of instruction: Lectures

## Examination Details

Examination formats: Written exam, written report
Examiner: