RINO: Robust INner and Outer Approximated Reachability of Neural Networks Controlled Systems

Abstract We present a unified approach, implemented in the RINO tool, for computation of inner and outer-approximations reachable sets discrete-time continuous-time dynamical systems, possibly controlled by neural networks with differentiable activation functions. combines zonotopic set representation generalized mean-value AE extensions to compute under over-approximations robust range functions, applies these techniques particular case learning-enabled systems. The require an efficient accurate evaluation function its Jacobian respect inputs initial conditions. For networks, evaluate is solution system. It over-approximated using Taylor methods time coupled set-based zonotopes. demonstrate good performances compared state-of-the art tools Verisig 2.0 ReachNN* on classical benchmark examples network closed loop generally comparable precision higher than ReachNN*, always at least one order magnitude faster, while also computing more involved inner-approximations that other do not compute.