Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs

Mario Villanueva, Boris Houska and Benoît Chachuat ()

Journal of Global Optimization, 2015, vol. 62, issue 3, 575-613

Abstract: 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. Copyright Springer Science+Business Media New York 2015

Keywords: Interval analysis; Ellipsoidal calculus; Taylor models; Ordinary differential equations; Differential inequalities; Convergence analysis; Dynamic optimization; Global optimization (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-014-0235-6

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