This paper is concerned with bounding the reachable set of parametric nonlinear ordinary differential equations using set-valued integration methods. The focus is on discrete-time set-propagation algorithms that proceed by first constructing a predictor of the reachable set and then determine a step-size for which this predictor yields a valid enclosure. For asymptotically stable systems, we give general conditions under which the computed bounds are stable, at least for small enough parametric variations. We also propose a strategy accounting for possible invariants of the dynamic system in order to further enhance stability. These novel developments are illustrated by means of numerical examples.
On the Stability of Set-Valued Integration for Parametric Nonlinear ODEs
Villanueva, Mario E.;
2014-01-01
Abstract
This paper is concerned with bounding the reachable set of parametric nonlinear ordinary differential equations using set-valued integration methods. The focus is on discrete-time set-propagation algorithms that proceed by first constructing a predictor of the reachable set and then determine a step-size for which this predictor yields a valid enclosure. For asymptotically stable systems, we give general conditions under which the computed bounds are stable, at least for small enough parametric variations. We also propose a strategy accounting for possible invariants of the dynamic system in order to further enhance stability. These novel developments are illustrated by means of numerical examples.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.