Construction of Parametric Barrier Functions for Dynamical Systems using Interval Analysis

A Djaballah (1) , Alexandre Chapoutot (1) , Michel Kieffer (2) , O Bouissou (3)

1 SFL - Sûreté et Fiabilité des Logiciels
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 LMeASI - Laboratoire Modélisation et Analyse de Systèmes en Interaction

Recently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe subset in which the state can be proved to remain and the complementary subset containing some unsafe region. This approach does not require any reachability analysis, but needs the computation of a valid barrier function, which is difficult when considering general nonlinear systems and barriers. This paper presents a new approach for the construction of barrier functions for nonlinear dynamical systems. The proposed technique searches for the parameters of a parametric barrier function using interval analysis. Complex dynamics can be considered without needing any relaxation of the constraints to be satisfied by the barrier function.

Mots clés: Formal verification; Dynamic systems; Intervals; Constraint satisfaction problem

Domaines: Automatique; Systèmes dynamiques [math.DS]; Systèmes et contrôle [cs.SY]

A Djaballah, Alexandre Chapoutot, Michel Kieffer, O Bouissou. Construction of Parametric Barrier Functions for Dynamical Systems using Interval Analysis. 2015. ⟨hal-01164307v1⟩