Balanced realizations of finite dimensional time invariant dynamical systems

Thiele, Michael

Balanced realizations of finite dimensional time invariant dynamical systems

Files

Thiele_2-gcf6ni62133i3.pdf(1.05 MB)

Date

2021

Publication type

Bachelor thesis

Publication status

Published

Abstract

In this thesis we demonstrate, how to receive a balanced realization of a finite dimensional linear time invariant (FDLTI) dynamical system. For that purpose we use the discretized heat equation as an application. We get such a balanced realization by following the algorithms in Robust and Optimal Control. So first we make the system observable, by applying one such algorithm and afterwards we make it controllable with a dual one. Then we have a minimal realization. From this point on we can apply a balancing algorithm to get a balanced realization. An important role in these algorithms plays the Lyapunov equation. In the controllability as well as the observability algorithm, we start by solving a Lyapunov equation. For these equations, we implemented the Lyapunov solver presented in Krylov subspace methods for large Lyapunov equations. This Lyapunov solver is based on a low rank block Krylov approximation. The way to a balanced realization connects this Lyapunov solver with the well known control theory of FDLTI dynamical systems.

Subject (DDC)

510 Mathematics

Keywords

Balanced realizations of FDLTI, block Krylov methods for solving large Lyapunov equations

Cite This

ISO 690

THIELE, Michael, 2021. Balanced realizations of finite dimensional time invariant dynamical systems [Bachelor thesis]. Konstanz: Universität Konstanz

BibTex

@mastersthesis{Thiele2021Balan-54846,
  year={2021},
  title={Balanced realizations of finite dimensional time invariant dynamical systems},
  address={Konstanz},
  school={Universität Konstanz},
  author={Thiele, Michael}
}

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University note

Konstanz, Universität Konstanz, Bachelor thesis, 2021