2 research outputs found
Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes
Over-approximating the reachable sets of dynamical systems is a fundamental
problem in safety verification and robust control synthesis. The representation
of these sets is a key factor that affects the computational complexity and the
approximation error. In this paper, we develop a new approach for
over-approximating the reachable sets of neural network dynamical systems using
adaptive template polytopes. We use the singular value decomposition of linear
layers along with the shape of the activation functions to adapt the geometry
of the polytopes at each time step to the geometry of the true reachable sets.
We then propose a branch-and-bound method to compute accurate
over-approximations of the reachable sets by the inferred templates. We
illustrate the utility of the proposed approach in the reachability analysis of
linear systems driven by neural network controllers
ReachLipBnB: A branch-and-bound method for reachability analysis of neural autonomous systems using Lipschitz bounds
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 directions of interest offline using a convex program. We then use
these bounds to obtain an instantaneous but conservative polyhedral
approximation of the reachable set using Lipschitz continuity arguments. To
reduce conservatism, we incorporate our bounding algorithm within a branching
strategy to decrease the over-approximation error within an arbitrary accuracy.
We then extend our method to reachability analysis of control systems with
neural network controllers. Finally, to capture the shape of the reachable sets
as accurately as possible, we use sample trajectories to inform the directions
of the reachable set over-approximations using Principal Component Analysis
(PCA). We evaluate the performance of the proposed method in several open-loop
and closed-loop settings