Imperial College London
Alternate

ProfessorBenoitChachuat

Faculty of Engineering, Department of Chemical Engineering

Professor of Process Systems Engineering
 
 
 
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Contact

 

b.chachuat Website

 
 
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Location

 

609Roderic Hill BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Houska:2015:10.1137/140976807,
author = {Houska, B and Villanueva, ME and Chachuat, B},
doi = {10.1137/140976807},
journal = {Siam Journal of Numerical Analysis},
pages = {2307--2328},
title = {Stable set-valued integration of nonlinear dynamic systems using affine set-parameterizations},
url = {http://dx.doi.org/10.1137/140976807},
volume = {53},
year = {2015}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Many set-valued integration algorithms for parametric ordinary differential equations (ODEs) implement a combination of Taylor series expansion with either interval arithmetic or Taylor model arithmetic. Due to the wrapping effect, the diameter of the solution-set enclosures computed with these algorithms typically diverges to infinity on finite integration horizons, even though the ODE trajectories themselves may be asymptotically stable. This paper starts by describing a new discretized set-valued integration algorithm that uses a predictor-validation approach to propagate generic affine set-parameterizations, whose images are guaranteed to enclose the ODE solution set. Sufficient conditions are then derived for this algorithm to be locally asymptotically stable, in the sense that the computed enclosures are guaranteed to remain stable on infinite time horizons when applied to a dynamic system in the neighborhood of a locally asymptotically stable periodic orbit (or equilibrium point). The key requirement here is quadratic Hausdorff convergence of function extensions in the chosen affine set-parameterization, which is proved to be the case, for instance, for Taylor models with ellipsoidal remainders. These stability properties are illustrated with the case study of a cubic oscillator system.
AU  - Houska,B
AU  - Villanueva,ME
AU  - Chachuat,B
DO  - 10.1137/140976807
EP  - 2328
PY  - 2015///
SN  - 0036-1429
SP  - 2307
TI  - Stable set-valued integration of nonlinear dynamic systems using affine set-parameterizations
T2  - Siam Journal of Numerical Analysis
UR  - http://dx.doi.org/10.1137/140976807
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000364456100009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/30358
VL  - 53
ER  -
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