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Publications of A. Davydov

Thesis

  1. A. Davydov. Contraction Theory in Control, Learning, and Optimization. PhD thesis, Mechanical Engineering Department, University of California at Santa Barbara, June 2025. PDF Keyword(s): Contraction Theory, Network Systems, Machine Learning, Neural Networks. [bibtex-entry]

Articles in journal or book chapters

  1. Y. Kawano, S. Betteti, A. Davydov, and F. Bullo. Incremental input-to-state stability and equilibrium tracking for stochastic contracting dynamics. IEEE Transactions on Automatic Control, 2026. Note: Submitted. Keyword(s): Contraction Theory. [bibtex-entry]
  2. S. Betteti, W. Retnaraj, A. Davydov, J. Cortes, and F. Bullo. Competition, Stability, and Functionality in Excitatory-Inhibitory Neural Circuits. Technical Report, 2025. Note: ArXiv:2512.05252. Keyword(s): Neural Networks. [bibtex-entry]
  3. A. Davydov, V. Centorrino, A. Gokhale, G. Russo, and F. Bullo. Time-Varying Convex Optimization: A Contraction and Equilibrium Tracking Approach. IEEE Transactions on Automatic Control, 70(11):7446-7460, 2025. Keyword(s): Contraction Theory. [bibtex-entry]
  4. A. Davydov, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Contraction Analysis of Continuous-Time Neural Networks. IEEE Transactions on Automatic Control, 70(1):235-250, 2025. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  5. R. Shima, A. Davydov, and F. Bullo. Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities. arXiv preprint arXiv:2503.20177, 2025. [bibtex-entry]
  6. V. Centorrino, A. Davydov, A. Gokhale, G. Russo, and F. Bullo. On Weakly Contracting Dynamics for Convex Optimization. IEEE Control Systems Letters, 8:1745-1750, 2024. Keyword(s): Contraction Theory. [bibtex-entry]
  7. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Positive Competitive Networks for Sparse Reconstruction. Neural Computation, 36(6):1163–1197, 2024. Keyword(s): Contraction Theory, Neural Networks, Theoretical Neuroscience. [bibtex-entry]
  8. A. Davydov and F. Bullo. Exponential Stability of Parametric Optimization-Based Controllers via Lur'e contractivity. IEEE Control Systems Letters, 8:1277-1282, 2024. Keyword(s): Contraction Theory. [bibtex-entry]
  9. A. Davydov and F. Bullo. Perspectives on Contractivity in Control, Optimization and Learning. IEEE Control Systems Letters, 8:2087-2098, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  10. A. Davydov, S. Jafarpour, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Monotone Operator Theory and Applications. Journal of Machine Learning Research, 25(307):1-33, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  11. A. Gokhale, A. Davydov, and F. Bullo. Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications. IEEE Control Systems Letters, 8:2853-2858, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  12. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Euclidean Contractivity of Neural Networks with Symmetric Weights. IEEE Control Systems Letters, 7:1724-1729, 2023. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  13. A. Gokhale, A. Davydov, and F. Bullo. Contractivity of Distributed Optimization and Nash Seeking Dynamics. IEEE Control Systems Letters, 7:3896-3901, 2023. [bibtex-entry]
  14. S. Jafarpour, A. Davydov, and F. Bullo. Non-Euclidean Contraction Theory for Monotone and Positive Systems. IEEE Transactions on Automatic Control, 68(9):5653-5660, 2023. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  15. A. V. Proskurnikov, A. Davydov, and F. Bullo. The Yakubovich S-Lemma Revisited: Stability and Contractivity in Non-Euclidean Norms. SIAM Journal on Control and Optimization, 61(4):1955-1978, 2023. Keyword(s): Contraction Theory. [bibtex-entry]
  16. A. Davydov, S. Jafarpour, and F. Bullo. Non-Euclidean Contraction Theory for Robust Nonlinear Stability. IEEE Transactions on Automatic Control, 67(12):6667-6681, 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]

Conference articles

  1. W. Retnaraj, S. Betteti, A. Davydov, F. Bullo, and J. Cortés. Timescale Limits of Linear-Threshold Networks. In IEEE Conf. on Decision and Control, Honolulu, Hawaii, 2026. Note: To appear. [bibtex-entry]
  2. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Biologically Plausible Neural Networks for Sparse Reconstruction: A Normative Framework. In Workshop “Mathematics for Artificial Intelligence and Machine Learning”, Milan, Italy, january 2024. Note: Oral Presentation. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  3. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Towards a Top/Down Normative Framework for a Biologically Plausible Explanation of Neural Circuits: Application to Sparse Reconstruction Problems. In 5th International Convention on the Mathematics of Neuroscience and AI, Rome, Italy, May 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  4. S. Jaffe, A. Davydov, D. Lapsekili, A. K. Singh, and F. Bullo. Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees. In Advances in Neural Information Processing Systems, 2024. [bibtex-entry]
  5. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Contractivity of Symmetric Neural Networks for Non-negative Sparse Approximation. In CCS/Italy 2023 Italian Regional Conference on Complex Systems, Naples, Italy, october 2023. Note: Poster Presentation. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  6. A. Davydov, S. Jaffe, A. K. Singh, and F. Bullo. Retrieving $k$-Nearest Memories with Modern Hopfield Networks. In Neurips Workshop on Associative Memory and Hopfield Networks, December 2023. [bibtex-entry]
  7. A. Davydov, S. Jafarpour, M. Abate, F. Bullo, and S. Coogan. Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks. In IEEE Conf. on Decision and Control, Cancun, Mexico, 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  8. A. Davydov, S. Jafarpour, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks. In IEEE Conf. on Decision and Control, Cancun, Mexico, December 2022. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  9. A. Davydov, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Contractivity of Recurrent Neural Networks. In American Control Conference, Atlanta, USA, pages 1527-1534, May 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  10. S. Jafarpour, M. Abate, A. Davydov, F. Bullo, and S. Coogan. Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach. In Learning for Dynamics and Control Conference, June 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  11. S. Jafarpour, A. Davydov, M. Abate, F. Bullo, and S. Coogan. Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach. In ICML Workshop on Formal Verification of Machine Learning, July 2022. Keyword(s): Contraction Theory. [bibtex-entry]
  12. F. Bullo, P. Cisneros-Velarde, A. Davydov, and S. Jafarpour. From Contraction Theory to Fixed Point Algorithms on Riemannian and non-Euclidean Spaces. In IEEE Conf. on Decision and Control, December 2021. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  13. S. Jafarpour, A. Davydov, A. V. Proskurnikov, and F. Bullo. Robust Implicit Networks via Non-Euclidean Contractions. In Advances in Neural Information Processing Systems, volume 34, pages 9857--9868, December 2021. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]

Miscellaneous

  1. R. Shima, A. Gokhale, A. Davydov, and F. Bullo. Regularized Model Predictive Control via Contractivity and Implicit Luré Analysis, September 2025. Note: Working Document. [bibtex-entry]

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