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Neural Networks (NNs) can provide major empirical performance improvementsfor robotic systems, but they also introduce challenges in formally analyzingthose systems' safety properties. In particular, this work focuses onestimating the forward reachable set of closed-loop systems with NNcontrollers. Recent work provides bounds on these reachable sets, yet thecomputationally efficient approaches provide overly conservative bounds (thuscannot be used to verify useful properties), whereas tighter methods are toointensive for online computation. This work bridges the gap by formulating aconvex optimization problem for reachability analysis for closed-loop systemswith NN controllers. While the solutions are less tight than prior semidefiniteprogram-based methods, they are substantially faster to compute, and some ofthe available computation time can be used to refine the bounds through inputset partitioning, which more than overcomes the tightness gap. The proposedframework further considers systems with measurement and process noise, thusbeing applicable to realistic systems with uncertainty. Finally, numericalcomparisons show $10\times$ reduction in conservatism in $\frac{1}{2}$ of thecomputation time compared to the state-of-the-art, and the ability to handlevarious sources of uncertainty is highlighted on a quadrotor model.

Efficient Reachability Analysis of Closed-Loop Systems with Neural Network Controllers