Linear control systems: reachability, observability, stability, realization theory, minimality, feedback, pole-assignment, observers. Linear-quadratic optimal control, matrix Riccati equation and theory for the algebraic Riccati equation. Kalman filtering.
FSF3832 Mathematical Systems Theory 7.5 credits
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About course offering
For course offering
Autumn 2023 Start 30 Oct 2023 programme students
Target group
PhD students only.
Part of programme
No information insertedPeriods
P2 (7.5 hp)Duration
Pace of study
50%
Form of study
Normal Daytime
Language of instruction
English
Course location
KTH Campus
Number of places
Places are not limited
Planned modular schedule
Course memo
Course memo is not publishedSchedule
Link to scheduleApplication
For course offering
Autumn 2023 Start 30 Oct 2023 programme students
Application code
51348
Contact
For course offering
Autumn 2023 Start 30 Oct 2023 programme students
Contact
Xiaoming Hu (hu@kth.se)
Examiner
No information insertedCourse coordinator
No information insertedTeachers
No information insertedContent and learning outcomes
Course contents
Intended learning outcomes
The overall goal of the course is to provide an understanding of the basic ingredients of linear systems theory and how these are used in analysis and design of control, estimation and filtering systems. In the course we take the state-space approach, which is well suited for efficient control and estimation design.
To pass the course, the student should be able to do the following:
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Analyze the state-space model with respect to minimality, observability, reachability, detectability and stabilizability.
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Explain the relationship between input-output (external) models and state-space (internal) models for linear systems and derive such models from the basic principles.
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Derive a minimal state-space model using the Kalman decomposition.
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Use algebraic design methods for state feedback design with pole assignment, and construct stable state observers by pole assignment and analyze the properties of the closed loop system obtained when the observer and the state feedback are combined to an observer based controller. Apply linear quadratic techniques to derive optimal state feedback controllers. Design a Kalman filter for optimal state estimation of linear systems subject to stochastic disturbances.
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Solve the Riccati equations that appear in optimal control and estimation problems.
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Apply the methods given in the course to solve example problems, including to use the Control System Toolbox in Matlab.
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Integrate the tools learnt during the course and apply them to more complex problems.
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Explain how the above results and methods relate and build on each other.
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Explain the mathematical (mainly linear algebra) foundations of the techniques used in linear systems theory and apply those techniques flexibly to variations of the problems studied in the course.
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Solve fairly simple but realistic control design problems using the methods in the course.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in in Mathematics (Calculus, Linear algebra, Differential equations and transform method), and further at least 6 hp in Mathematical Statistics, 6 hp in Numerical analysis and 6 hp in Optimization.
Recommended prerequisites
Equipment
Literature
Compendiumfrom the department.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- PRO1 - Project work, 1.5 credits, grading scale: P, F
- TEN1 - Written exam, 6.0 credits, grading scale: P, 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.
Project, Written examination, Exercises.
Other requirements for final grade
Project, Written examination, Optional homeworks give bonus credits on written examination.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
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.