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

2025-12-01

AI Summary

Verifying closed-loop contraction of neural network controllers for nonlinear systems remains challenging. Method: We propose a provably stable end-to-end learning framework that introduces a scalable sufficient condition for contraction based on the principal eigenvalue of symmetric Metzler matrices, integrated with interval analysis and domain partitioning to embed contraction constraints directly into training. Contraction metric and neural controller are jointly optimized via interval-bound propagation and parameterized metric learning. Contribution/Results: This work is the first to couple Metzler matrix spectral properties with domain-partitioned verification, enabling seamless integration of training and formal verification. Experiments on an inverted pendulum demonstrate that the learned controller strictly satisfies closed-loop contraction, guaranteeing global exponential stability. The approach significantly enhances verifiability and generalization robustness of neural control policies.

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• Intelligent Robots: Behavior Learning & Control
• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Learning to Search

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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.

Problem

• Verifying closed-loop contractivity in neural network-controlled nonlinear systems
• Providing a scalable sufficient condition using interval analysis and partitioning
• Learning provably contractive neural network controllers and metrics

Innovation

• Interval analysis for verifying neural network controllers
• Domain partitioning strategy integrated into training process
• Sufficient condition based on symmetric Metzler matrix eigenvalues