Ensuring safety is crucial for the successful deployment of autonomous systems, such as self-
driving vehicles, unmanned aerial vehicles, and robots acting close to humans. While there …

Reachability analysis is a formal method to guarantee safety of dynamical systems under the
influence of uncertainties. A substantial bottleneck of all reachability algorithms is the …

We present a novel approach to compute non-convex inner-approximations of reachable
sets for nonlinear continuous systems. The concept of our approach is to extract inner …

Backward reachability analysis is essential to synthesizing controllers that ensure the
correctness of closed-loop systems. This article is concerned with developing scalable …

We describe a set-based approach, relying on mean-value extensions, for computing
guaranteed under-approximations of ranges (or images) of continuously differentiable …

In the context of developing safe air transportation, our work is focused on understanding
how Reinforcement Learning methods can improve the state of the art in traditional control …

Reachability analysis, in general, is a fundamental method that supports formally-correct
synthesis, robust model predictive control, set-based observers, fault detection, invariant …

We investigate the problem of data-driven, on-the-fly control of systems with unknown
nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side …

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

Inner-approximate reachability analysis involves calculating subsets of reachable sets,
known as inner-approximations. This analysis is crucial in the fields of dynamic systems …