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
Lessons
| 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
| 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 |
Prerequisites
| 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 |