A Constraint Programming Approach for Polytopic Simulation of Ordinary Differential Equations:

Julien Alexandre dit Sandretto; Alexandre Chapoutot; Christophe Garion; Xavier Thirioux

doi:10.14232/actacyb.300771

Julien Alexandre dit Sandretto ENSTA Paris, Institut Polytechnique de Paris, Palaiseau, France https://orcid.org/0000-0002-6185-2480
Alexandre Chapoutot ENSTA Paris, Institut Polytechnique de Paris, Palaiseau, France https://orcid.org/0000-0002-7230-0710
Christophe Garion ISAE-SUPAERO, Université de Toulouse, Toulouse, France https://orcid.org/0000-0002-4467-2939
Xavier Thirioux ISAE-SUPAERO, Université de Toulouse, Toulouse, France https://orcid.org/0009-0002-1126-6835

DOI: https://doi.org/10.14232/actacyb.300771

Keywords: constraint programming, abstract domains, ordinary differential equations, cyber-physical systems, abstract interpretation

Abstract

This paper presents a constraint-based approach to compute the reachable tube of nonlinear differentiable equations. A set of initial values for the equations is considered and defined by a polytope represented as intersections of zonotopes. Guaranteed numerical integration based on zonotopic computation is used to compute reachable tubes. In order to efficiently build polytopes defined by the intersection of several zonotopes, we use a previously developed abstract domain to represent reachable tubes. The proposed contribution allows to compute more expressive reachable tubes more efficiently than methods based only on boxes, and therefore could improve verification/validation processes in robotics application for example. The approach is evaluated on examples taken from literature and we present two applications of this work.

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A Constraint Programming Approach for Polytopic Simulation of Ordinary Differential Equations

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