Related papers: Neural Continuous-Time Supermartingale Certificate…
This paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The aim is to ascertain lower and upper bounds of the probability that, within a predefined finite-time horizon, a system…
In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time…
In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of…
In this paper, we propose a system-level approach for verifying the safety of neural network controlled systems, combining a continuous-time physical system with a discrete-time neural network based controller. We assume a generic model for…
Ensuring string stability is critical for the safety and efficiency of large-scale interconnected systems. Although learning-based controllers (e.g., those based on reinforcement learning) have demonstrated strong performance in complex…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…
In this paper, we propose a data-driven approach to formally verify the safety of (potentially) unknown discrete-time continuous-space stochastic systems. The proposed framework is based on a notion of barrier certificates together with…
We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.…
We introduce a functional inductive framework to verify discrete-time dynamical systems against hyperproperties specified as Hyperlinear temporal logic formulae via a notion of HyperCertificates. Unlike linear temporal logic (LTL) formulae…
The possibility of errors in human-engineered formal verification software, such as model checkers, poses a serious threat to the purpose of these tools. An established approach to mitigate this problem are certificates -- lightweight,…
Recent advances in deep learning have enabled the development of autonomous systems that use deep neural networks for perception. Formal verification of these systems is challenging due to the size and complexity of the perception DNNs as…
To create usable and deployable Artificial Intelligence (AI) systems, there requires a level of assurance in performance under many different conditions. Many times, deployed machine learning systems will require more classic logic and…
Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed…
We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems. Specifically, we consider linear time-invariant models whose state space matrices are known only…
This paper presents tailor-made neural model structures and two custom fitting criteria for learning dynamical systems. The proposed framework is based on a representation of the system behavior in terms of continuous-time state-space…
Developing stable controllers for large-scale networked dynamical systems is crucial but has long been challenging due to two key obstacles: certifiability and scalability. In this paper, we present a general framework to solve these…
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity…
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…
Reinforcement learning (RL) methods have demonstrated their efficiency in simulation environments. However, many applications for which RL offers great potential, such as autonomous driving, are also safety critical and require a certified…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…