Related papers: Policy Verification in Stochastic Dynamical System…

Lipschitz constant is a fundamental property in certified robustness, as smaller values imply robustness to adversarial examples when a model is confident in its prediction. However, identifying the worst-case adversarial examples is known…

Markov Decision Processes (MDPs) are a classical model for decision making in the presence of uncertainty. Often they are viewed as state transformers with planning objectives defined with respect to paths over MDP states. An increasingly…

This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However…

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust…

A wide range of learning tasks require human input in labeling massive data. The collected data though are usually low quality and contain inaccuracies and errors. As a result, modern science and business face the problem of learning from…

Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs,…

Reinforcement learning combined with sim-to-real transfer offers a general framework for developing locomotion controllers for legged robots. To facilitate successful deployment in the real world, smoothing techniques, such as low-pass…

Ensuring scalable input-to-state stability (sISS) is critical for the safety and reliability of large-scale interconnected systems, especially in the presence of communication delays. While learning-based controllers can achieve strong…

We study the verification problem of stochastic systems under signal temporal logic (STL) specifications. We propose a novel approach that enables the verification of the probabilistic satisfaction of STL specifications for nonlinear…

Neural Lyapunov and barrier certificates have recently been used as powerful tools for verifying the safety and stability properties of deep reinforcement learning (RL) controllers. However, existing methods offer guarantees only under…

Reach-Avoid-Stay (RAS) optimal control enables systems such as robots and air taxis to reach their targets, avoid obstacles, and stay near the target. However, current methods for RAS often struggle with handling complex, dynamic…

This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…

We present a method for feedback motion planning of systems with unknown dynamics which provides probabilistic guarantees on safety, reachability, and goal stability. To find a domain in which a learned control-affine approximation of the…

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…

This paper studies satisfying temporal logic specifications on stochastic dynamical systems, where the predicates evolve randomly over time. Such randomness may arise from uncertain environment models or external stochastic processes…

Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions,…

We propose a method for data-driven practical stabilization of nonlinear systems with provable guarantees, based on the concept of Nonparametric Chain Policies (NCPs). The approach employs a normalized nearest-neighbor rule to assign, at…

This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…

We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…