Bracketing Backward Reach Sets Of A Dynamical System

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 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.