  This paper presents a new approach to design verified compositions of Neural
Network (NN) controllers for autonomous systems with tasks captured by Linear
Temporal Logic (LTL) formulas. Particularly, the LTL formula requires the
system to reach and avoid certain regions in a temporal/logical order. We
assume that the system is equipped with a finite set of trained NN controllers.
Each controller has been trained so that it can drive the system towards a
specific region of interest while avoiding others. Our goal is to check if
there exists a temporal composition of the trained NN controllers - and if so,
to compute it - that will yield composite system behaviors that satisfy a
user-specified LTL task for any initial system state belonging to a given set.
To address this problem, we propose a new approach that relies on a novel
integration of automata theory and recently proposed reachability analysis
tools for NN-controlled systems. We note that the proposed method can be
applied to other controllers, not necessarily modeled by NNs, by appropriate
selection of the reachability analysis tool. We focus on NN controllers due to
their lack of robustness. The proposed method is demonstrated on navigation
tasks for aerial vehicles.
