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Towards a Generic Interval Solver for Differential-Algebraic CSP

Simon Rohou 1 Abderahmane Bedouhene 2 Gilles Chabert 3 Alexandre Goldsztejn 4 Luc Jaulin 1 Bertrand Neveu 2 Victor Reyes 5 Gilles Trombettoni 5
1 Lab-STICC_ENSTAB_CID_PRASYS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
5 COCONUT - Agents, Apprentissage, Contraintes
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In this paper, we propose an interval constraint programming approach that can handle the differential-algebraic CSP (DACSP), where an instance is composed of real and functional variables (also called dynamic variables or trajectories) together, and differential and/or “static” numerical constraints among those variables. Differential-Algebraic CSP systems can model numerous real-life problems occurring in physics, biology or robotics. We introduce a solver, built upon the Tubex and Ibex interval libraries, that can rigorously approximate the set of solutions of a DACSP system. The solver achieves temporal slicing and a tree search by splitting trajectories domains. Our approach provides a significant step towards a generic interval CP solver for DACSP that has the potential to handle a large variety of constraints. First experiments highlight that this solver can tackle interval Initial Value Problems (IVP), Boundary Value Problems (BVP) and integro-differential equations.
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Submitted on : Saturday, October 3, 2020 - 12:00:18 PM
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Simon Rohou, Abderahmane Bedouhene, Gilles Chabert, Alexandre Goldsztejn, Luc Jaulin, et al.. Towards a Generic Interval Solver for Differential-Algebraic CSP. International Conference on Principles and Practice of Constraint Programming (CP), Simonis, Helmut, Sep 2020, Louvain-la-Neuve, Belgium. pp.548-565, ⟨10.1007/978-3-030-58475-7_32⟩. ⟨hal-02956402⟩

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