Related papers: A New Framework for Bounding Reachability Probabil…
In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. While the extension of the analysis to a…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
In this paper we propose novel optimization-based methods for verifying reach-avoid (or, eventuality) properties of continuous-time systems modelled by ordinary differential equations. Given a system, an initial set, a safe set and a target…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an…
Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the system state stays in a safe region (e.g., to avoid…
We present a new stochastic framework for studying ship capsize. It is a synthesis of two strands of transition state theory. The first is an extension of deterministic transition state theory to dissipative non-autonomous systems, together…
In this paper we propose sufficient conditions to synthesizing reach-avoid controllers for deterministic systems modelled by ordinary differential equations and stochastic systems modeled by stochastic differential equations based on the…
We provide certificates for almost sure reachability of continuous-time stochastic systems governed by stochastic differential equations (SDEs). We first show that a standard Euler-Maruyama discretization may fail to preserve almost sure…
In this paper, we study Stochastic Control Barrier Functions (SCBFs) to enable the design of probabilistic safe real-time controllers in presence of uncertainties and based on noisy measurements. Our goal is to design controllers that bound…
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…
In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
This paper presents a safe controller synthesis of discrete-time stochastic systems using Control Barrier Functions (CBFs). The proposed condition allows the design of a safe controller synthesis that ensures system safety while avoiding…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…