On the Stability of Set-Valued Integration for Parametric Nonlinear ODEs

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.