Computing ODE-barriers in hyper-rectangles
Stefan Ratschan · 2016
In this paper we develop a computationally cheap, but incomplete method for computing barriers of ordinary differential equations. We consider a barrier of an ODE to be a subset of the state-space such that no trajectory of the ODE can start inside of the barrier and end outside. We compute barriers that may serve as a certificate that no trajectory may lead from a given face of a hyper-rectangle to the opposite face. Such a method can be useful for more involved techniques for analyzing dynamical systems, especially for techniques based on abstraction.