Barrier certificates revisited

Barrier Certificates Revisited

A barrier certificate can separate the state space of a considered hybrid system (HS) into safe and unsafe parts according to the safety property to be verified. Therefore this notion has been widely used in the verification of HSs. A stronger condition on barrier certificates means that less expressive barrier certificates can be synthesized. On the other hand, synthesizing more expressive bar...

On the Necessity of Barrier Certificates

A methodology for safety verification of nonlinear systems using barrier certificates has been proposed recently. The condition was stated in a sufficiency form: if there exists a barrier certificate, then the system is safe, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. Using the concepts of convex duality and density f...

Barrier certificates for nonlinear model validation

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a datadriven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system w...

Safety Verification of Hybrid Systems Using Barrier Certificates

This paper presents a novel methodology for safety verification of hybrid systems. For proving that all trajectories of a hybrid system do not enter an unsafe region, the proposed method uses a function of state termed a barrier certificate. The zero level set of a barrier certificate separates the unsafe region from all possible trajectories starting from a given set of initial conditions, hen...