Reachability analysis consists in computing the set of states that are reachable by a
dynamical system from all initial states and for all admissible inputs and parameters. It is a …

One of the biggest boosts for innovation in engineering has been the ongoing improvement
of digital processor technology. Connections between physical systems and computing …

In this paper, we define relational abstractions of hybrid systems. A relational abstraction is
obtained by replacing the continuous dynamics in each mode by a binary transition relation …

In this thesis, we present the three novel set representations sparse polynomial zonotopes,
constrained polynomial zonotopes, and the Z-representation of polytopes. One major …

Template polyhedra generalize intervals and octagons to polyhedra whose facets are
orthogonal to a given set of arbitrary directions. They have been employed in the abstract …

We examine linear programming (LP) based relaxations for synthesizing polynomial
Lyapunov functions to prove the stability of polynomial ordinary differential equations …

This paper is concerned with the reachability computation problem for polynomial discrete-
time dynamical systems. Such computations constitute a crucial component in algorithmic …

In this paper we propose a new method for reachability analysis of the class of discrete-time
polynomial dynamical systems. Our work is based on the approach combining the use of …

We present abstraction techniques that transform a given non-linear dynamical system into a
linear system, such that, invariant properties of the resulting linear abstraction can be used …

We present the results of a friendly competition for formal verification of continuous and
hybrid systems with nonlinear continuous dynamics. The friendly competition took place as …