8 research outputs found
Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
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 horizon, if the system is safe, it, starting from a compact initial
set, will remain within an open and bounded safe region throughout the
specified time horizon, regardless of the disturbances. The main contribution
of this work is to uncover that there exists a time-dependent barrier
certificate if and only if the system is safe. This barrier certificate
satisfies the following conditions: negativity over the initial set at the
initial time instant, non-negativity over the boundary of the safe set, and
non-increasing behavior along the system dynamics over the specified finite
time horizon. The existence problem is explored using a Hamilton-Jacobi
differential equation, which has a unique Lipschitz viscosity solution
Lyapunov-Barrier Characterization of Robust Reach-Avoid-Stay Specifications for Hybrid Systems
Stability, reachability, and safety are crucial properties of dynamical
systems. While verification and control synthesis of reach-avoid-stay
objectives can be effectively handled by abstraction-based formal methods, such
approaches can be computationally expensive due to the use of state-space
discretization. In contrast, Lyapunov methods qualitatively characterize
stability and safety properties without any state-space discretization. Recent
work on converse Lyapunov-barrier theorems also demonstrates an approximate
completeness or verifying reach-avoid-stay specifications of systems modelled
by nonlinear differential equations. In this paper, based on the topology of
hybrid arcs, we extend the Lyapunov-barrier characterization to more general
hybrid systems described by differential and difference inclusions. We show
that Lyapunov-barrier functions are not only sufficient to guarantee
reach-avoid-stay specifications for well-posed hybrid systems, but also
necessary for arbitrarily slightly perturbed systems under mild conditions.
Numerical examples are provided to illustrate the main results
Learning safe neural network controllers with barrier certificates
We provide a new 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 functions, which are represented by NNs as well. We train the controller-NN and barrier-NN simultaneously, achieving a verification-in-the-loop synthesis. We provide a prototype tool nncontroller with a number of case studies. The experiment results confirm the feasibility and efficacy of our approach