Intervallmethoden zur Berechnung exponentieller Zustandseinschlüsse für die Erreichbarkeitsanalyse unsicherer Systeme (Artikel)

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Intervallmethoden zur Berechnung exponentieller Zustandseinschlüsse für die Erreichbarkeitsanalyse unsicherer Systeme (Artikel)
Autor Andreas Rauh, Julia Kersten, Ekaterina Auer, Harald Aschemann
In: at - Automatisierungstechnik
Ausgabe 68 (10)
ISBN/ISSN: 2196-677X
Erscheinungsjahr 2020
Jahrgang
Seitenzahl 826--839
Hyperlink https://doi.org/10.1515/auto-2019-0065
Review peer

The computation of guaranteed state enclosures has a large variety of applications in engineering. Possible application scenarios involve the simulation-based verification of linear and nonlinear feedback controllers as well as the implementation of model-predictive control procedures. In many of these applications, system models can be derived in a control-oriented form by first-principle techniques so that they are characterized by a dominant linear part (commonly after a suitable coordinate transformation) with a not fully negligible nonlinear part. To compute guaranteed state enclosures for such systems, general purpose approaches relying on a Taylor series expansion of the solution can be employed. However, such procedures do not exploit specific knowledge about the structure of the system model at hand, such as quasi-linearity and stability. To incorporate these structural properties for real-life scenarios in an effective way, an exponential state enclosure technique is presented in this paper. Starting with a real-valued implementation for systems with aperiodic dynamics, a generalization is presented which makes use of complex-valued state enclosures for systems with oscillatory behavior. Possibilities to extend the presented method towards fractional-order differential equations conclude this paper.