Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints

• URL: http://arxiv.org/abs/2505.22889v1
• Date: Wed, 28 May 2025 21:45:49 GMT
• Title: Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints
• Authors: Hamidreza Montazeri Hedesh, Moh Kamalul Wafi, Milad Siami,
• Abstract summary: We study the local stability of nonlinear systems in the Lur'e form with static nonlinear feedback realized by feedforward neural networks (FFNNs)<n>By leveraging positivity system constraints, we employ a localized variant of the Aizerman conjecture, which provides sufficient conditions for exponential stability of trajectories confined to a compact set.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the local stability of nonlinear systems in the Lur'e form with static nonlinear feedback realized by feedforward neural networks (FFNNs). By leveraging positivity system constraints, we employ a localized variant of the Aizerman conjecture, which provides sufficient conditions for exponential stability of trajectories confined to a compact set. Using this foundation, we develop two distinct methods for estimating the Region of Attraction (ROA): (i) a less conservative Lyapunov-based approach that constructs invariant sublevel sets of a quadratic function satisfying a linear matrix inequality (LMI), and (ii) a novel technique for computing tight local sector bounds for FFNNs via layer-wise propagation of linear relaxations. These bounds are integrated into the localized Aizerman framework to certify local exponential stability. Numerical results demonstrate substantial improvements over existing integral quadratic constraint-based approaches in both ROA size and scalability.

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