Noyau de viabilité: une contrainte globale pour la modélisation de systèmes dynamiques

This paper presents an approach to handle some problems arising in the modelling of hybrid systems combining static and dynamic. In the case of a discrete or continuous dynamic system, there is no particular condition forcing a solution of a differential inclusion starting from a point x0 to remain in a set K defined by a set of static constraints. We study the subsets of K containing only the points such that at least one solution starting from them will stay in K forever. The largest subset of K containing all such points is called the “viability kernel” of K, and the operator transforming K into V iab(K) is a propagation operator. This allows the notion of viability to be introduced as a global constraint which enables us to model certain hybrid problems defined as a combination of classic constraints with a dynamic system. MOTS-CLÉS : Programmation par contraintes, système hybride, théorie de la viabilité.