# SF2842 Geometric Control Theory 7.5 credits

### Choose semester and course offering

Choose semester and course offering to see information from the correct course syllabus and course offering.

Headings with content from the Course syllabus SF2842 (Spring 2022–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Invariance and controlled invariance
• V* and disturbance decoupling
• Zeros, Zero dynamics and system inversion
• Tracking and non-interacting control
• Input-output behavior
• Output regulation, Internal model principle
• Nonlinear systems

### Intended learning outcomes

After having completed the course the student shall be able to:

• Interpret and explain basic properties of linear systems from a geometric perspective.
• Apply different algorithms to solve control problems such as DDP, non-interacting control, tracking and outputregulation.
• Solve some basic control problems for nonlinear systems that do not have a controllable linearized system.

In addition, for the highest grade the student shall be able to:

• Solve simple but realistic control problems that require synthesis of different design algorithms.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

English B / English 6

In general:

150 university credits (hp) including 28 hp in Mathematics, 6 hp in Mathematical Statistics and 6 hp in Control Theory. Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis, control theory. A passed course in mathematical systems theory (SF2832) is an advantage.

### Recommended prerequisites

Completed course SF2832 Mathematical systems theory or equivalent.

### Equipment

No information inserted

### Literature

Geometric Control Theory, lecture notes by Hu and Lindquist.

## 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 - Home assignments, 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 web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2842

Mathematics

Second cycle