%0 Conference Proceedings
%T Towards a Generic Interval Solver for Differential-Algebraic CSP
%+ Lab-STICC_ENSTAB_CID_PRASYS
%+ Laboratoire d'Informatique Gaspard-Monge (LIGM)
%+ Institut de Recherche Technologique Jules Verne [Bouguenais] (IRT Jules Verne)
%+ Laboratoire des Sciences du Numérique de Nantes (LS2N)
%+ Agents, Apprentissage, Contraintes (COCONUT)
%A Rohou, Simon
%A Bedouhene, Abderahmane
%A Chabert, Gilles
%A Goldsztejn, Alexandre
%A Jaulin, Luc
%A Neveu, Bertrand
%A Reyes, Victor
%A Trombettoni, Gilles
%< avec comité de lecture
%( Principles and Practice of Constraint Programming<br>26th International Conference, CP 2020, Louvain-la-Neuve, Belgium, September 7–11, 2020, Proceedings
%B CP 2020 - 26th International Conference on Principles and Practice of Constraint Programming
%C Louvain-la-Neuve, Belgium
%I Springer
%3 Lecture Notes in Computer Science (LNCS)
%V 12333
%P 548-565
%8 2020-09-07
%D 2020
%R 10.1007/978-3-030-58475-7_32
%K Interval Analysis
%K Constraint programming
%K Differential Algebraic Equations
%Z Engineering Sciences [physics]
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Computer Science [cs]/Artificial Intelligence [cs.AI]Conference papers
%X 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.
%G English
%2 https://hal-ensta-bretagne.archives-ouvertes.fr/hal-02956402/document
%2 https://hal-ensta-bretagne.archives-ouvertes.fr/hal-02956402/file/dacsp_paper.pdf
%L hal-02956402
%U https://hal-ensta-bretagne.archives-ouvertes.fr/hal-02956402
%~ UNIV-BREST
%~ UNIV-NANTES
%~ INSTITUT-TELECOM
%~ ENSTA-BRETAGNE
%~ ENPC
%~ CNRS
%~ UNIV-UBS
%~ EC-NANTES
%~ LIGM_A3SI
%~ ENSTA-BRETAGNE-STIC
%~ INSMI
%~ PARISTECH
%~ LIGM
%~ UNAM
%~ ENIB
%~ COCONUT
%~ ARITH
%~ LAB-STICC
%~ LIRMM
%~ TDS-MACS
%~ LS2N
%~ LS2N-OGRE
%~ MIPS
%~ UNIV-MONTPELLIER
%~ INSTITUTS-TELECOM
%~ ANR
%~ UNIV-EIFFEL
%~ U-EIFFEL
%~ NANTES-UNIVERSITE
%~ UNIV-NANTES-AV2022
%~ NU-CENTRALE
%~ UM-2015-2021