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

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  • Mario Villanueva
  • Boris Houska
  • Benoît Chachuat

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

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  • Mario Villanueva & Boris Houska & Benoît Chachuat, 2015. "Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs," Journal of Global Optimization, Springer, vol. 62(3), pages 575-613, July.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:3:p:575-613
    DOI: 10.1007/s10898-014-0235-6
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    References listed on IDEAS

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    Cited by:

    1. Ishan Bajaj & M. M. Faruque Hasan, 2020. "Global dynamic optimization using edge-concave underestimator," Journal of Global Optimization, Springer, vol. 77(3), pages 487-512, July.
    2. Spencer D. Schaber & Joseph K. Scott & Paul I. Barton, 2019. "Convergence-order analysis for differential-inequalities-based bounds and relaxations of the solutions of ODEs," Journal of Global Optimization, Springer, vol. 73(1), pages 113-151, January.

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