Bracketing backward reach sets of a dynamical system

Thomas Le Mézo (1, 2) , Luc Jaulin (1, 2) , Benoit Zerr (1, 2)

1 Lab-STICC_ENSTAB_CID_PRASYS
2 ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne

In this paper, we present a new method for bracketing (i.e., characterizing from inside and from outside) backward reach set of the target region T of a continuous time dynamical system. The principle of the method is to formalize the problem as a constraint network, where the variables are the trajectories (or paths) of the system. The resolution is made possible by using mazes which is a set of paths that contain all solutions of the problem. As a result, we will be able to derive a method able to compute a backward reach set for a huge class of systems without any knowledge of a parametric Lyapunov function and without assuming any linearity for our system. The method will be illustrated on several examples.

Mots clés: Abstract interpretation; Backward reach set; Basin of attraction; Stability; Constraint solving; Interval Computation

Domaines: Systèmes dynamiques [math.DS]; Automatique / Robotique

Thomas Le Mézo, Luc Jaulin, Benoit Zerr. Bracketing backward reach sets of a dynamical system. International Journal of Control, 2020, 93 (11), pp.2528-2540. ⟨10.1080/00207179.2019.1643910⟩. ⟨hal-02190303⟩