Symmetry Groups and the Observability of PDEs

Bernd Kolar; Markus Schöberl

doi:10.1002/pamm.201800019

Symmetry Groups and the Observability of PDEs

Bernd Kolar, Markus Schöberl

Institute of Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.

Original language	English
Title of host publication	Proceedings in Applied Mathematics and Mechanics
Publisher	Wiley
Number of pages	2
Volume	18
DOIs	https://doi.org/10.1002/pamm.201800019
Publication status	Published - Dec 2018

Fields of science

202017 Embedded systems
203015 Mechatronics
101028 Mathematical modelling
202 Electrical Engineering, Electronics, Information Engineering
202003 Automation
202027 Mechatronics
202034 Control engineering

JKU Focus areas

Mechatronics and Information Processing

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10.1002/pamm.201800019

System-theoretic Analysis and Controller Design for PDEs
Kolar, B. (Researcher), Malzer, T. (Researcher) & Schöberl, M. (PI)
01.05.2017 → 31.10.2021
Project: Funded research › FWF - Austrian Science Fund

Cite this

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title = "Symmetry Groups and the Observability of PDEs",

abstract = "Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.",

author = "Bernd Kolar and Markus Sch{\"o}berl",

year = "2018",

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doi = "10.1002/pamm.201800019",

language = "English",

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T1 - Symmetry Groups and the Observability of PDEs

AU - Kolar, Bernd

AU - Schöberl, Markus

PY - 2018/12

Y1 - 2018/12

N2 - Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.

AB - Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.

U2 - 10.1002/pamm.201800019

DO - 10.1002/pamm.201800019

M3 - Conference proceedings

VL - 18

BT - Proceedings in Applied Mathematics and Mechanics

PB - Wiley

ER -

Symmetry Groups and the Observability of PDEs

Abstract

Fields of science

JKU Focus areas

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Projects

System-theoretic Analysis and Controller Design for PDEs

Cite this