Towards a Generic Interval Solver for Differential-Algebraic CSP
Simon Rohou, Abderahmane Bedouhene , Gilles Chabert, Alexandre Goldsztejn, Luc Jaulin, Bertrand Neveu, Victor Reyes, Gilles Trombettoni
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.