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BibTex format

author = {Villanueva, ME and Houska, B and Chachuat, B},
doi = {10.1007/s10898-014-0235-6},
journal = {Journal of Global Optimization},
pages = {575--613},
title = {Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs},
url = {},
volume = {62},
year = {2014}

RIS format (EndNote, RefMan)

AB - This paper presents a framework for constructing and analyzing enclosures ofthe reachable set of nonlinear ordinary differential equations using continuous-time setpropagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. A generalized differential inequality is introduced, whose solutionsdescribe such support functions for a convex enclosure of the reachable set under mild conditions. It is shown that existing continuous-time bounding methods that are based on standard differential inequalities or ellipsoidal set propagation techniques can be recovered as special cases of this generalized differential inequality. A way of extending this approach for the construction of nonconvex enclosures is also described, which relies on Taylor modelswith convex remainder bounds. This unifying framework provides a means for analyzing the convergence properties of continuous-time enclosure methods. The enclosure techniques and convergence results are illustrated with numerical case studies throughout the paper, including a six-state dynamic model of anaerobic digestion.
AU - Villanueva,ME
AU - Houska,B
AU - Chachuat,B
DO - 10.1007/s10898-014-0235-6
EP - 613
PY - 2014///
SN - 1573-2916
SP - 575
TI - Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs
T2 - Journal of Global Optimization
UR -
UR -
UR -
VL - 62
ER -