Title | ||
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Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs |
Abstract | ||
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This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations using continuous-time set-propagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. A generalized differential inequality is introduced, whose solutions describe 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 models with 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. |
Year | DOI | Venue |
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2015 | 10.1007/s10898-014-0235-6 | Journal of Global Optimization |
Keywords | Field | DocType |
Interval analysis,Ellipsoidal calculus,Taylor models,Ordinary differential equations,Differential inequalities,Convergence analysis,Dynamic optimization,Global optimization | Convergence (routing),Mathematical optimization,Nonlinear system,Enclosure,Ordinary differential equation,Global optimization,Mathematical analysis,Computer science,Remainder,Parametric statistics,Interval arithmetic | Journal |
Volume | Issue | ISSN |
62 | 3 | 0925-5001 |
Citations | PageRank | References |
12 | 0.59 | 29 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Mario Eduardo Villanueva | 1 | 33 | 6.10 |
Boris Houska | 2 | 214 | 26.14 |
Benoît Chachuat | 3 | 125 | 10.89 |