# SF2852 Optimal Control Theory 7.5 credits

### Choose semester and course offering

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## Application

### For course offering

Autumn 2024 Start 26 Aug 2024 programme students

### Application code

51870

Headings with content from the Course syllabus SF2852 (Spring 2022–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Dynamic programming in continuous and discrete time.
• Hamilton-Jacobi-Bellman equation.
• Theory of ordinary differential equations.
• The Pontryagin maximum principle.
• Infinite horizon optimal control problems.
• Model predictive control.
• Numerical methods for optimal control problems.

### Intended learning outcomes

To pass the course, the student shall be able to do the following:

• Formulate optimal control problems on standard form from specifications on dynamics, constraints and control objective. In addition, be able to explain how various control objectives affect the optimal performance.
• Use the methods in the course to design closed loop and open loop controllers for optimal control problems.
• Apply the methods given in the course to solve example problems and use computational software to solve realistic problems numerically.

• Combine and explain the tools of the course and apply them to more complex problems.

## Literature and preparations

### Specific prerequisites

• English B / English 6
• Completed basic course in optimization (SF1811, SF1861 or equivalent)
• Completed basic course in mathematical statistics (SF1914, SF1918, SF1922 or equivalent)
• Completed basic course in numerical analysis (SF1544, SF1545 or equivalent)
• Completed basic course in differential equations (SF1633, SF1683 or equivalent).

### Recommended prerequisites

A completed course in control theory.

### Equipment

No information inserted

### Literature

No information inserted

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• HEM2 - Homework, 1.5 credits, grading scale: P, F
• TEN2 - Written exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Mathematics

Second cycle