Name
Title | ||
|---|---|---|
A validated integration algorithm for nonlinear ODEs using Taylor models and ellipsoidal calculus |
Abstract | ||
|---|---|---|
This paper presents a novel algorithm for bounding the reachable set of parametric nonlinear differential equations. This algorithm is based on a first-discretize-then-bound approach to enclose the reachable set via propagation of a Taylor model with ellipsoidal remainder, and it accounts for truncation errors that are inherent to the discretization. In contrast to existing algorithms that proceed in two phases-an a priori enclosure phase, followed by a tightening phase-the proposed algorithm first predicts a continuous-time enclosure and then seeks a maximal step-size for which validity of the predicted enclosure can be established. It is shown that this reversed approach leads to a natural step-size control mechanism, which no longer relies on the availability of an a priori enclosure. Also described in the paper is an open-source implementation of the algorithm in ACADO Toolkit. A simple numerical case study is presented to illustrate the performance and stability of the algorithm. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/CDC.2013.6759928 | Decision and Control |
Keywords | Field | DocType |
convex programming,iterative methods,nonlinear differential equations,numerical stability,reachability analysis,set theory,ACADO Toolkit,Taylor model propagation,a priori enclosure phase,continuous-time enclosure,ellipsoidal calculus,ellipsoidal remainder,first-discretize-then-bound approach,maximal step-size,natural step-size control mechanism,nonlinear ODE,open-source implementation,parametric nonlinear differential equations,reachable set,tightening phase,truncation errors,validated integration algorithm | Discretization,Mathematical optimization,Nonlinear system,Ordinary differential equation,Computer science,Control theory,Iterative method,A priori and a posteriori,Parametric statistics,Truncation error (numerical integration),Numerical stability | Conference |
ISSN | ISBN | Citations |
0743-1546 | 978-1-4673-5714-2 | 5 |
PageRank | References | Authors |
0.42 | 9 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Houska | 1 | 214 | 26.14 |
| Mario Eduardo Villanueva | 2 | 33 | 6.10 |
| Benoît Chachuat | 3 | 125 | 10.89 |