Stochastic hybrid systems have received significant attentions as a relevant modeling
framework describing many systems, from engineering to the life sciences: they enable the …

Controllers for dynamical systems that operate in safety-critical settings must account for
stochastic disturbances. Such disturbances are often modeled as process noise in a …

We present for the first time a supermartingale certificate for ω-regular specifications. We
leverage the Robbins & Siegmund convergence theorem to characterize supermartingale …

We consider the policy synthesis problem for continuous-state controlled Markov processes
evolving in discrete time, when the specification is given as a Büchi condition (visit a set of …

Stochastic processes are expressive mathematical tools for modeling real-world systems
that are subject to uncertainty. It is hence crucial to be able to formally analyze the behavior …

Ensuring safety through set invariance has proven a useful method in a variety of
applications in robotics and control. In this paper, we focus on the safe probabilistic …

We study distributional reachability for finite Markov decision processes (MDPs) from a
control theoretical perspective. Unlike standard probabilistic reachability notions, which are …

This paper focuses on optimizing probabilities of events of interest defined over general
controlled discrete-time Markov processes. It is shown that the optimization over a wide …

Martingale theory yields a powerful set of tools that have recently been used to prove
quantitative properties of stochastic systems such as stochastic safety and qualitative …

The goal of this work is to formally abstract a Markov process evolving in discrete time over a
general state space as a finite-state Markov chain, with the objective of precisely …