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

TL;DR

This paper introduces a convex optimization-based method for fast, less conservative reachability analysis of closed-loop systems with neural network controllers, effectively handling uncertainties and enabling real-time safety verification.

Contribution

It proposes a computationally efficient convex optimization framework that balances tightness of bounds with speed, improving over existing methods for neural network-controlled systems.

Findings

10x reduction in conservatism compared to state-of-the-art

Half the computation time of previous methods

Effective handling of measurement and process noise

Abstract

Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the forward reachable set of closed-loop systems with NN controllers. Recent work provides bounds on these reachable sets, yet the computationally efficient approaches provide overly conservative bounds (thus cannot be used to verify useful properties), whereas tighter methods are too intensive for online computation. This work bridges the gap by formulating a convex optimization problem for reachability analysis for closed-loop systems with NN controllers. While the solutions are less tight than prior semidefinite program-based methods, they are substantially faster to compute, and some of the available computation time can be used to refine the bounds through input set partitioning, which more than overcomes the tightness gap. The proposed framework further considers systems with measurement and process noise, thus being applicable to realistic systems with uncertainty. Finally, numerical comparisons show $10\times$ reduction in conservatism in $\frac{1}{2}$ of the computation time compared to the state-of-the-art, and the ability to handle various sources of uncertainty is highlighted on a quadrotor model.