MAT-62507 Mathematical Control Theory, 5 cr

Additional information

The course evaluation is based on a final exam and an (optional but recommended) final project work.
Suitable for postgraduate studies.

Person responsible

Lassi Paunonen


Implementation Period Person responsible Requirements
MAT-62507 2019-01 2 Lassi Paunonen
Completed final exam, weekly exercises, and (an optional) course project. For details on the topics and grading, see the POP page for the course.

Learning Outcomes

The course covers the basic theory of linear, time invariant dynamical systems from the time-domain and frequency-domain point of view. Topics covered include controllability, observability, stabilization, and optimal control. The first half of the course concentrates on control of finite-dimensional systems and the second half on control infinite-dimensional linear systems. The theory is illustrated with examples involving controlled ordinary and partial differential equations, most notably controlled mechanical systems, groups of moving robots, as well as controlled heat, diffusion and vibration processes. Matlab is used to approximate and simulate the control systems.


Content Core content Complementary knowledge Specialist knowledge
1. Fundamental properties and typical applications of finite-dimensional linear control theory.  Ability to formulate simple differential equation models as linear control systems.  Analysis of mathematical models in the control theoretic framework. 
2. Concepts of controllability, observability, and stabilizability.  Characterizations of the concepts for finite-dimensional systems.  Understanding of the proof of the main results. 
3. Fundamentals of linear dynamic partial differential equation models and semigroup theory.  Formulating of processes modeled by dynamic partial differential equations as control systems.  Analysis of the existence of solutions of dynamic PDE models using semigroup theory. 
4. Controllability, observability and stabilizability of controlled linear PDE models.  Application of the concepts in the study of diffusion and wave equations.  Understanding the technical details of the proofs. 
5. Using Matlab/Python in controller design and simulation of PDE control systems.  Capability of using the course codes for controller design and analysis of linear systems.  Capability of writing simple progams for approximation and control design for controlled PDE models. 

Study material

Type Name Author ISBN URL Additional information Examination material
Book   A Short Course on Operator Semigroups   Klaus-Jochen Engel and Rainer Nagel       Supplementary material on semigroup theory. Freely available through TUNI Library.   No   
Book   An Introduction to Infinite-Dimensional Linear Systems Theory   Ruth Curtain and Hans Zwart       Background material on semigroup theory and the operator-theoretic approach to control of partial differential equations.   No   
Book   Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces   Birgit Jacob and Hans Zwart       Background material covering many of the same topics as the main lecture material.   No   
Summary of lectures   Mathematical Control Theory   Lassi Paunonen       Freely available for students. Previous version: "Lassi Paunonen - Linear Systems".   Yes   


Course Mandatory/Advisable Description
MAT-60100 Kompleksimuuttujan funktiot Mandatory   1
MAT-60106 Complex Analysis Mandatory   1
MAT-60000 Matriisilaskenta Mandatory   2
MAT-60006 Matrix Algebra Mandatory   2
MAT-60150 Differentiaaliyhtälöt Mandatory    
MAT-60206 Mathematical Analysis Advisable    
MAT-61007 Introduction to Functional Analysis Advisable    

1 . MAT-60100 Kompleksimuuttujan funktiot or MAT-60106 Complex Analysis

2 . MAT-60000 Matriisilaskenta or MAT-60006 Matrix Algebra

Correspondence of content

Course Corresponds course  Description 
MAT-62507 Mathematical Control Theory, 5 cr MAT-62506 Linear Systems, 5 cr  

Updated by: Kunnari Jaana, 05.03.2019