1,840 research outputs found

    Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes

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    Artificial neural networks (ANNs) have been utilized in many feedback control systems and introduced new challenges regarding the safety of the system. This paper considers the problem of verifying whether the trajectories of a system with a feedforward neural network (FNN) controller can avoid unsafe regions, using a constrained zonotope-based reachability analysis approach. FNNs with the rectified linear unit activation function are considered in this work. A novel set-based method is proposed to compute both exact and over-approximated reachable sets for linear discrete-time systems with FNN controllers, and linear program-based sufficient conditions are presented to certify the safety of the neural feedback systems. Reachability analysis and safety verification for neural feedback systems with nonlinear models are also considered. The computational efficiency and accuracy of the proposed method are demonstrated by two numerical examples where a comparison with state-of-the-art methods is also provided.Comment: 8 pages, 4 figure

    Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming

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    There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these systems is challenging due to the nonlinear and compositional structure of neural networks. In this paper, we propose a novel forward reachability analysis method for the safety verification of linear time-varying systems with neural networks in feedback interconnection. Our technical approach relies on abstracting the nonlinear activation functions by quadratic constraints, which leads to an outer-approximation of forward reachable sets of the closed-loop system. We show that we can compute these approximate reachable sets using semidefinite programming. We illustrate our method in a quadrotor example, in which we first approximate a nonlinear model predictive controller via a deep neural network and then apply our analysis tool to certify finite-time reachability and constraint satisfaction of the closed-loop system

    Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes

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    Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets. We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers

    Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

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    In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.Comment: 8 pages, 9 figures, to appear in TNNL
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