On the stability of set-valued integration for parametric nonlinear ODEs


  • M.E. Villanueva, B. Houska, B. Chachuat


  • Computer Aided Chemical Engineering,
    Volume 33, pages 595 - 600, 2014.


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.


author = {M.E. Villanueva and B. Houska and B. Chachuat},
title = {On the stability of set-valued integration for parametric nonlinear ODEs},
journal = {Computer Aided Chemical Engineering},
year = {2014},
volume = {33},
pages = {595–600}