Related papers: A Framework for Safe Probabilistic Invariance Veri…

This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and…

Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…

Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…

Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…

A fundamental challenge in learning to control an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn…

This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high…

We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we…

In this paper, we consider the use of barrier function-based approaches for the safe control problem in stochastic systems. With the presence of stochastic uncertainties, a myopic controller that ensures safe probability in infinitesimal…

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 dynamical system, and common assumptions are that the underlying…

We study black-box testing for stochastic systems and arbitrary $\omega$-regular specifications, explicitly including liveness properties. We are given a finite-state probabilistic system that we can only execute from the initial state. We…

The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…

We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…

Uncertainties influencing the dynamical systems pose a significant challenge in estimating the achievable performance of a controller aiming to control such uncertain systems. When the uncertainties are of stochastic nature, obtaining hard…

Safety in stochastic control systems, which are subject to random noise with a known probability distribution, aims to compute policies that satisfy predefined operational constraints with high confidence throughout the uncertain evolution…

Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…

We incorporate safety specifications into dynamic programming. Explicitly, we address the minimization problem of a Markov decision process up to a stopping time with safety constraints. To incorporate safety into dynamic programming, we…

Generating accurate runtime safety estimates for autonomous systems is vital to ensuring their continued proliferation. However, exhaustive reasoning about future behaviors is generally too complex to do at runtime. To provide scalable and…

We present a model predictive control (MPC) framework for nonlinear stochastic systems that ensures safety guarantee with high probability. Unlike most existing stochastic MPC schemes, our method adopts a set-erosion that converts the…

Combining efficient and safe control for safety-critical systems is challenging. Robust methods may be overly conservative, whereas probabilistic controllers require a trade-off between efficiency and safety. In this work, we propose a…