Related papers: Barrier Certificates Revisited
Barrier certificates play an important role in verifying the safety of continuous-time systems, including autonomous driving, robotic manipulators and other critical applications. Recently, ReLU neural barrier certificates -- barrier…
In this paper, we introduce two new types of barrier certificates that are based on multiple functions rather than a single one. A conventional barrier certificate for a stochastic dynamical system is a nonnegative real-valued function…
An emerging branch of control theory specialises in certificate learning, concerning the specification of a desired (possibly complex) system behaviour for an autonomous or control model, which is then analytically verified by means of a…
We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust…
A dynamical system is strongly robustly safe provided that it remains safe in the presence of a continuous and positive perturbation, named robustness margin, added to both the argument and the image of the right-hand side (the dynamics).…
The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming…
This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing…
The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing…
This paper introduces the notion of control closure certificates to synthesize controllers for discrete-time control systems against $\omega$-regular specifications. Typical functional approaches to synthesize controllers against…
The rapid integration of AI algorithms in safety-critical applications such as autonomous driving and healthcare is raising significant concerns about the ability to meet stringent safety standards. Traditional tools for formal safety…
This paper establishes the equivalence between robust safety and the existence of a barrier function certificate for differential inclusions. More precisely, for a robustly-safe differential inclusion, a barrier function is constructed as…
We consider the problem of safety verification and safety-aware controller synthesis for systems with sector bounded nonlinearities. We aim to keep the states of the system within a given safe set under potential actuator and sensor…
Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem that limits the wider adoption of autonomous systems in safety-critical applications. One promising solution to address this problem…
Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial…
We provide two certificates of convexity for arbitrary basic semi-algebraic sets of $\R^n$. The first one is based on a necessary and sufficient condition whereas the second one is based on a sufficient (but simpler) condition only. Both…
The control of complex systems faces a trade-off between high performance and safety guarantees, which in particular restricts the application of learning-based methods to safety-critical systems. A recently proposed framework to address…
In this paper, we compare several representative barrier-like conditions from the literature for infinite-horizon reach-avoid verification of stochastic discrete-time systems. Our comparison examines both their theoretical properties and…
Verified controller synthesis uses world models that comprise all potential behaviours of humans, robots, further equipment, and the controller to be synthesised. A world model enables quantitative risk assessment, for example, by…
We provide a novel approach to synthesize controllers for nonlinear continuous dynamical systems with control against safety properties. The controllers are based on neural networks (NNs). To certify the safety property we utilize barrier…
While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary…