Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioning

• URL: http://arxiv.org/abs/2512.02262v1
• Date: Mon, 01 Dec 2025 23:06:56 GMT
• Title: Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioning
• Authors: Alexander Davydov,
• Abstract summary: We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks.<n>We derive a tractable and scalable sufficient condition for closed-loop contractivity that reduces to checking that the dominant eigenvalue of a symmetric Metzler matrix is nonpositive.
• Score: 52.23804865017831
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks. By leveraging interval analysis and interval bound propagation, we derive a tractable and scalable sufficient condition for closed-loop contractivity that reduces to checking that the dominant eigenvalue of a symmetric Metzler matrix is nonpositive. We combine this sufficient condition with a domain partitioning strategy to integrate this sufficient condition into training. The proposed approach is validated on an inverted pendulum system, demonstrating the ability to learn neural network controllers and contraction metrics that provably satisfy the contraction condition.

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