Intervallmethoden zur Berechnung exponentieller Zustandseinschlüsse für die Erreichbarkeitsanalyse unsicherer Systeme (Artikel)
|Intervallmethoden zur Berechnung exponentieller Zustandseinschlüsse für die Erreichbarkeitsanalyse unsicherer Systeme (Artikel)|
|Autor||Andreas Rauh, Julia Kersten, Ekaterina Auer, Harald Aschemann|
|In:||at - Automatisierungstechnik|
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.