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    Area of Science:

    • Artificial Intelligence
    • Control Theory
    • Robotics

    Background:

    • Multilayer perceptron (MLP) neural networks are increasingly used in safety-critical systems.
    • Verifying the safety and predicting the behavior of MLPs remains a significant challenge.
    • Existing methods often struggle with scalability and automation.

    Purpose of the Study:

    • To develop methods for output reachable set estimation in MLPs.
    • To enable automated safety verification for neural network-controlled systems.
    • To introduce the concept of maximum sensitivity for MLP analysis.

    Main Methods:

    • Introduced 'maximum sensitivity' for analyzing MLPs with monotonic activation functions.
    • Formulated output reachable set estimation as a series of convex optimization problems.
    • Developed an automated safety verification framework based on reachable set estimation.

    Main Results:

    • Maximum sensitivity is efficiently computable for a class of MLPs using convex optimization.
    • A simulation-based approach effectively estimates the output reachable set.
    • Automated safety verification was successfully demonstrated on a two-joint robotic arm model.

    Conclusions:

    • The proposed methods provide effective tools for analyzing MLP behavior and ensuring system safety.
    • The approach is applicable to real-world robotic systems, enhancing their reliability.
    • This work advances the field of neural network verification and safety assurance.