Model-Free Verification for Neural Network Controlled Systems
arxiv(2023)
摘要
Neural network controllers have shown potential in achieving superior
performance in feedback control systems. Although a neural network can be
trained efficiently using deep and reinforcement learning methods, providing
formal guarantees for the closed-loop properties is challenging. The main
difficulty comes from the nonlinear activation functions. One popular method is
to use sector bounds on the activation functions resulting in a robust
analysis. These methods work well under the assumption that the system dynamics
are perfectly known, which is, however, impossible in practice. In this paper,
we propose data-driven semi-definite programs to formally verify stability and
safety for a neural network controlled linear system with unknown dynamics. The
proposed method performs verification directly from end-to-end without
identifying the dynamics. Through a numerical example, we validate the efficacy
of our method on linear systems with controller trained by imitation learning.
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