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In recent years, deep reinforcement learning (DRL) approaches have generated highly successful controllers for a myriad of complex domains. However, the opaque nature of these models limits their applicability in aerospace systems and sasfety-critical domains, in which a single mistake can have dire consequences. In this paper, we present novel advancements in both the training and verification of DRL controllers, which can help ensure their safe behavior. We showcase a design-for-verification approach utilizing k-induction and demonstrate its use in verifying liveness properties. In addition, we also give a brief overview of neural Lyapunov Barrier certificates and summarize their capabilities on a case study. Finally, we describe several other novel reachability-based approaches which, despite failing to provide guarantees of interest, could be effective for verification of other DRL systems, and could be of further interest to the community. 

Neural network approximations have become attractive to compress data for automation and autonomy algorithms for use on storage-limited and processing-limited aerospace hardware. However, unless these neural network approximations can be exhaustively verified to be safe, they cannot be certified for use on aircraft. An example of such systems is the unmanned Airborne Collision Avoidance System (ACAS) Xu, which is a very popular benchmark for open-loop neural network control system verification tools. This paper proposes a new closed-loop extension of this benchmark, which consists of a set of 10 closed-loop properties selected to evaluate the safety of an ownship aircraft in the presence of a co-altitude intruder aircraft. These closed-loop safety properties are used to evaluate five of the 45 neural networks that comprise the ACAS Xu benchmark (corresponding to co-altitude cases) as well as the switching logic between the five neural networks. The combination of nonlinear dynamics and switching between five neural networks is a challenging verification task accomplished with star-set reachability methods in two verification tools. The safety of the ownship aircraft under initial position uncertainty is guaranteed in every scenario proposed. 

Neural network approximations have become attractive to compress data for automation and autonomy algorithms for use on storage-limited and processing-limited aerospace hard-ware. However, unless these neural network approximations can be exhaustively verified to be safe, they cannot be certified for use on aircraft. This manuscript evaluates the safety of a neural network approximation of the unmanned Airborne Collision Avoidance System (ACAS Xu). First, a set of ACAS Xu closed-loop benchmarks is introduced, based on a well-known open-loop benchmark, that are challenging to analyze for current verification tools due to the complexity and high-dimensional plant dynamics. Additionally, the system of switching and classification-based nature of the ACAS Xu neural network system adds another challenge to existing analysis methods. Experimental evaluation shows selected scenarios where the safety of the ownship aircraft’s neural network action selection is assessed with respect to an intruder aircraft over time in a closed loop control evaluation. Set-based analysis of the closed-loop benchmarks is performed using the Star Set representation using both the NNV tool and the nnenum tool, demonstrating that set-based analysis is becoming increasingly feasible for the verification of this class of systems.