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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. 

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2021. In the third edition of this AINNCS category at ARCH-COMP, three tools have been applied to solve seven different benchmark problems, (in alphabetical order): JuliaReach, NNV, and Verisig. JuliaReach is a new participant in this category, Verisig participated previously in 2019 and NNV has participated in all previous competitions. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results combined with 2020 results probably provide the most complete assessment of current tools for safety verification of NNCS.

 

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. 

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. In the second edition of this AINNCS category at ARCH-COMP, four tools have been applied to solve seven different benchmark problems, (in alphabetical order): NNV, OVERT, ReachNN*, and VenMAS. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results probably provide the most complete assessment of current tools for safety verification of NNCS.