  Neural networks (NNs) have been shown to learn complex control laws
successfully, often with performance advantages or decreased computational cost
compared to alternative methods. Neural network controllers (NNCs) are,
however, highly sensitive to disturbances and uncertainty, meaning that it can
be challenging to make satisfactory robustness guarantees for systems with
these controllers. This problem is exacerbated when considering multi-agent
NN-controlled systems, as existing reachability methods often scale poorly for
large systems. This paper addresses the problem of finding overapproximations
of forward reachable sets for discrete-time uncertain multi-agent systems with
distributed NNC architectures. We first reformulate the dynamics, making the
system more amenable to reachablility analysis. Next, we take advantage of the
distributed architecture to split the overall reachability problem into smaller
problems, significantly reducing computation time. We use quadratic
constraints, along with a convex representation of uncertainty in each agent's
model, to form semidefinite programs, the solutions of which give
overapproximations of forward reachable sets for each agent. Finally, the
methodology is tested on two realistic examples: a platoon of vehicles and a
power network system.
