# MAT-62507 Mathematical Control Theory, 5 cr

#### Lisätiedot

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

Lassi Paunonen

#### Opetus

 Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset 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.

#### Osaamistavoitteet

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.

#### Sisältö

 Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys 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.

#### Oppimateriaali

 Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali 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

#### Esitietovaatimukset

 Opintojakso P/S Selite 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

#### Vastaavuudet

 Opintojakso Vastaa opintojaksoa Selite MAT-62507 Mathematical Control Theory, 5 cr MAT-62506 Linear Systems, 5 cr

 Päivittäjä: Kunnari Jaana, 05.03.2019