Bracketing backward reach sets of a dynamical system

Abstract

In this paper, we present a new method for bracketing (i.e. characterising from inside and from outside) backward reach set of the target region $\mathbb{T}$ of a continuous-time dynamical system. The principle of the method is to formalise 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 in several examples.

Keywords:

• Abstract interpretation
• backward reach set
• basin of attraction
• stability
• constraint solving
• interval computation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the French Government Defense procurement and technology agency (Direction Générale de l’Armement). It also benefited from the support of the project CONTREDO of the French National Research Agency (Agence Nationale de la Recherche) (ANR-16-CE33-0024).