An Interval Constraint Programming Approach for Quasi Capture Tube Validation - École des Ponts ParisTech Access content directly
Conference Papers Acta Chimica Slovenica Year : 2021

An Interval Constraint Programming Approach for Quasi Capture Tube Validation


Proving that the state of a controlled nonlinear system always stays inside a time moving bubble (or capture tube) amounts to proving the inconsistency of a set of nonlinear inequalities in the time-state space. In practice however, even with a good intuition, it is difficult for a human to find such a capture tube except for simple examples. In 2014, Jaulin et al. established properties that support a new interval approach for validating a quasi capture tube, i.e. a candidate tube (with a simple form) from which the mobile system can escape, but into which it enters again before a given time. A quasi capture tube is easy to find in practice for a controlled system. Merging the trajectories originated from the candidate tube yields the smallest capture tube enclosing it. This paper proposes an interval constraint programming solver dedicated to the quasi capture tube validation. The problem is viewed as a differential CSP where the functional variables correspond to the state variables of the system and the constraints define system trajectories that escape from the candidate tube "for ever". The solver performs a branch and contract procedure for computing the trajectories that escape from the candidate tube. If no solution is found, the quasi capture tube is validated and, as a side effect, a corrected smallest capture tube enclosing the quasi one is computed. The approach is experimentally validated on several examples having 2 to 5 degrees of freedom. 2012 ACM Subject Classification Applied computing → Operations research; Mathematics of computing → Ordinary differential equations; Mathematics of computing → Differential algebraic equations; Mathematics of computing → Interval arithmetic; Theory of computation → Constraint and logic programming
Fichier principal
Vignette du fichier
An_Interval_Constraint_Programming_Approach_for_Quasi_Capture_Tube_Validation.pdf (1.91 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03412799 , version 1 (16-02-2022)



Abderahmane Bedouhene, Bertrand Neveu, Gilles Trombettoni, Luc Jaulin, Stéphane Le Ménec. An Interval Constraint Programming Approach for Quasi Capture Tube Validation. CP 2021 - 27th International Conference on Principles and Practice of Constraint Programming, Oct 2021, Montpellier, France. pp.18:1--18:17, ⟨10.4230/LIPIcs.CP.2021.18⟩. ⟨hal-03412799⟩
106 View
29 Download



Gmail Facebook Twitter LinkedIn More