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

Created by
  • Haebom

Author

Hamidreza Montazeri Hedesh, Moh Kamalul Wafi, Milad Siami

Outline

This paper studies the local stability of Lur'e-form nonlinear systems with static nonlinear feedback implemented using feedforward neural networks (FFNNs). We exploit positivity system constraints and use a localized variant of the Aizerman conjecture to provide sufficient conditions for exponential stability of trajectories confined to a compact set. Building on this, we develop two methods for estimating the Region of Attraction (ROA). First, a less conservative Lyapunov-based approach constructs invariant sublevel sets of quadratic functions satisfying linear matrix inequality (LMI). Second, a novel technique for computing strict local sector boundaries for FFNNs via layer-by-layer propagation of linear relaxations is presented. These boundaries are integrated into a localized Aizerman framework to verify local exponential stability. Numerical results demonstrate significant improvements over existing approaches based on integral quadratic constraints in terms of ROA size and scalability.

Takeaways, Limitations

Takeaways:
A novel approach to local stability analysis of nonlinear systems using FFNNs is presented.
Development of two effective methodologies for estimating ROA (Lyapunov-based and local sector boundary-based).
Numerically demonstrating improved ROA size and scalability compared to existing methodologies.
Limitations:
Limited to Lur'e type systems.
Focus on local stability analysis.
Further research is needed to determine applicability and generalizability to real systems.
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