mlsanityData to 7 Oct 2026

Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllers

arXiv 2406.12744 ↗First posted 18 Jun 2024eess.SY cs.AI cs.SYcited by 4

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Abstract (arXiv)

This paper introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without biases, we present a stability theorem that demonstrates the global exponential stability of linear systems under fully connected FFNN control. Utilizing principles from positive Lur'e systems and the positive Aizerman conjecture, our approach effectively addresses the challenge of ensuring stability in highly nonlinear systems. The crux of our method lies in maintaining sector bounds that preserve the positivity and Hurwitz property of the overall Lur'e system. We showcase the practical applicability of our methodology through its implementation in a linear system managed by a FFNN trained on output feedback controller data, highlighting its potential for enhancing stability in dynamic systems.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 15 of its 28 references that are in the map. First posted on arXiv 18 Jun 2024.

Builds on

15 of 28 references.

References · 15

  1. 2013Intriguing properties of neural networkscited by 5,114
  2. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  3. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  4. 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 148
  5. 2021Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificatescited by 71
  6. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 42
  7. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
  8. 2018Stability-certified reinforcement learning: A control-theoretic perspectivecited by 29
  9. 2020Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimizationcited by 17
  10. 2021Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systemscited by 15
  11. 2021DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splittingcited by 8
  12. 2022Stability of Non-linear Neural Feedback Loops using Sum of Squarescited by 6
3 more
  1. 2023Structured Neural-PI Control with End-to-End Stability and Output Tracking Guaranteescited by 5
  2. 2023Scalable Forward Reachability Analysis of Multi-Agent Systems with Neural Network Controllerscited by 3
  3. 2023On the ISS Property of the Gradient Flow for Single Hidden-Layer Neural Networks with Linear Activationscited by 1

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Cited by year

Citing papers per year: 2025: 4.

4 papers.

  1. 2025Robust Stability Analysis of Positive Lure System with Neural Network Feedbackcited by 2
  2. 2025Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraintscited by 2
  3. 2025Frequency Response Identification of Low-Order Systems: Finite-Sample Analysiscited by 0
  4. 2025Delay Independent Safe Control with Neural Networks: Positive Lur'e Certificates for Risk Aware Autonomycited by 0