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 …

Ellipsoids are a common representation for reachability analysis, because they can be
transformed efficiently under affine maps, and they allow conservative approximation of …

Neural networks are increasingly used in safety-critical applications such as robotics and
autonomous vehicles. However, the deployment of neural-network-controlled systems …

This tutorial provides a comprehensive perspective on the study of zonotopic filtering for
nonlinear uncertain dynamical systems. Unlike stochastic methods that characterize the …

Decision trees have gained popularity as interpretable surrogate models for learning-based
control policies. However, providing safety guarantees for systems controlled by decision …

Set-based methods have been leveraged in many engineering applications from robust
control and global optimization, to probabilistic planning and estimation. While useful, these …

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

This paper presents identities for calculating over-approximated successor sets of discrete-
time nonlinear systems using hybrid zonotopes. The proposed technique extends the state …

Optimizing a parameterized zonotope or ellipsoid is a common task in robust state
estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids …

Polynomial zonotopes, a non-convex set representation, have a wide range of applications
from real-time motion planning and control in robotics, to reachability analysis of nonlinear …