Verification of hybrid systems using Kaucher arithmetic
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Stefan Schwab
Stefan Schwab studied electrical engineering at the Karlsruhe Institute of Technology (KIT) and the University of Newcastle, Australia and received his Master’s degree from KIT in 2012. Afterwards he worked as research assistant at the Institute of Control Systems (IRS) at Karlsruhe Institute of Technology (KIT) and was fellow of the doctoral college “Projekthaus eDrive”. In 2018 he became department manager Control in Information Technology (CIT) at the Research Center for Information Technology (FZI) in Karlsruhe.
and
Soeren Hohmann
Soeren Hohmann studied electrical engineering at the Technische Universität Braunschweig, University of Karlsruhe and école nationale supérieure d’électricité et de mécanique Nancy. He received the diploma degree (1997) and Ph. D. degree (2002) from University of Karlsruhe. Afterwards, until 2010 he worked in the industry for BMW, Munich, where his last position was head of the predevelopement and series developement of active safety systems. Today he is the head of the Institute of Control Systems (IRS) at the Karlsruhe Institute of Technology (KIT) as well as a directors board member of the Research Center for Information Technology (FZI), Karlsruhe. His research interests are cooperative control, alternative energies and system guarantees by design.
Abstract
The increasing complexity of technical systems leads to increasing challenges regarding the verification of those systems. Especially in the context of safety critical systems, there is a high need for reliable verification results. Currently verification is mainly based on expert knowledge and the use of high performance hardware to investigate a very high amount of test cases. This article proposes an alternative approach using an iterating segmentation and identification algorithm that is appended by interval arithmetic calculations. This combination yields guaranteed results that do not suffer from type II failures, i. e., that will never verify an erroneous system. This is especially relevant in the context of safety critical systems.
Zusammenfassung
Die zunehmende Komplexität technischer Systeme führt zu immer größeren Problemen bei der Verifikation. Insbesondere im Kontext von sicherheitskritischen Systemen besteht ein großer Bedarf an zuverlässigen Verifikationsergebnisse. Aktuelle Verifikationsansätze basieren häufig auf Expertenwissen oder dem Einsatz von hoch performanter Hardware zur Untersuchung einer sehr großen Anzahl von Testfällen. Dieser Beitrag zeigt einen alternativen Ansatz basierend auf einen interativen Identifikations- und Segmentierungsalgorithmus. Der eingeführte Algorithmus wird anschließend auf intervalarithmetische Rechnung erweitert. Dadurch ist es möglich, mathematisch garantierte Ergebnisse zu erzielen, die keine Fehler zweiter Art erzeugen. Fehlerhafte Systeme werden somit niemals fälschlicherweise verifiziert. Diese Eigenschaft ist gerade im Kontext von sicherheitskritischen Systemen sehr wichtig.
Funding statement: This work was partially funded by ITK Engineering GmbH.
About the authors
Stefan Schwab studied electrical engineering at the Karlsruhe Institute of Technology (KIT) and the University of Newcastle, Australia and received his Master’s degree from KIT in 2012. Afterwards he worked as research assistant at the Institute of Control Systems (IRS) at Karlsruhe Institute of Technology (KIT) and was fellow of the doctoral college “Projekthaus eDrive”. In 2018 he became department manager Control in Information Technology (CIT) at the Research Center for Information Technology (FZI) in Karlsruhe.
Soeren Hohmann studied electrical engineering at the Technische Universität Braunschweig, University of Karlsruhe and école nationale supérieure d’électricité et de mécanique Nancy. He received the diploma degree (1997) and Ph. D. degree (2002) from University of Karlsruhe. Afterwards, until 2010 he worked in the industry for BMW, Munich, where his last position was head of the predevelopement and series developement of active safety systems. Today he is the head of the Institute of Control Systems (IRS) at the Karlsruhe Institute of Technology (KIT) as well as a directors board member of the Research Center for Information Technology (FZI), Karlsruhe. His research interests are cooperative control, alternative energies and system guarantees by design.
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Articles in the same Issue
- Frontmatter
- Methoden
- Stabilitätsgesicherte Stellgrößenbegrenzungsstrategie für beliebige zeitdiskrete PI-Zustandsregler bei linearen zeitinvarianten Systemen
- Uncertainty quantification of nonlinear distributed parameter systems using generalized polynomial chaos
- Control of NCSs with energy efficient channel assignment and power allocation
- Verification of hybrid systems using Kaucher arithmetic
- Anwendungen
- Umsetzung einer echtzeitfähigen modellprädiktiven Trajektorienplanung für eine mehrachsige Hybridkinematik auf einer Industriesteuerung
- Vergleich Impedanzregelung (IC) – Parallele Impedanzregelung (PIC) zur Kraft-/Impedanzregelung dynamischer Systeme
Articles in the same Issue
- Frontmatter
- Methoden
- Stabilitätsgesicherte Stellgrößenbegrenzungsstrategie für beliebige zeitdiskrete PI-Zustandsregler bei linearen zeitinvarianten Systemen
- Uncertainty quantification of nonlinear distributed parameter systems using generalized polynomial chaos
- Control of NCSs with energy efficient channel assignment and power allocation
- Verification of hybrid systems using Kaucher arithmetic
- Anwendungen
- Umsetzung einer echtzeitfähigen modellprädiktiven Trajektorienplanung für eine mehrachsige Hybridkinematik auf einer Industriesteuerung
- Vergleich Impedanzregelung (IC) – Parallele Impedanzregelung (PIC) zur Kraft-/Impedanzregelung dynamischer Systeme
