mlsanityData to 14 Oct 2026

Learning Robust State Observers using Neural ODEs (longer version)

arXiv 2212.00866 ↗First posted 1 Dec 2022eess.SY cs.LG cs.SYcited by 7

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Abstract (arXiv)

Relying on recent research results on Neural ODEs, this paper presents a methodology for the design of state observers for nonlinear systems based on Neural ODEs, learning Luenberger-like observers and their nonlinear extension (Kazantzis-Kravaris-Luenberger (KKL) observers) for systems with partially-known nonlinear dynamics and fully unknown nonlinear dynamics, respectively. In particular, for tuneable KKL observers, the relationship between the design of the observer and its trade-off between convergence speed and robustness is analysed and used as a basis for improving the robustness of the learning-based observer in training. We illustrate the advantages of this approach in numerical simulations.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 15 of its 31 references that are in the map. First posted on arXiv 1 Dec 2022.

Builds on

15 of 31 references.

References · 15

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2015Continuous control with deep reinforcement learningcited by 3,407
  4. 2022On Neural Differential Equationscited by 268
  5. 2020Dissecting Neural ODEscited by 153
  6. 2019Deep Learning via Dynamical Systems: An Approximation Perspectivecited by 78
  7. 2020Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODEcited by 76
  8. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 44
  9. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 41
  10. 2020Universal Approximation Power of Deep Residual Neural Networks via Nonlinear Control Theorycited by 18
  11. 2022Towards gain tuning for numerical KKL observerscited by 14
  12. 2022Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEscited by 13
3 more
  1. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  2. 2022Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systemscited by 11
  3. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 3.

7 papers.

  1. 2024Nonlinear Discrete-Time Observers with Physics-Informed Neural Networkscited by 8
  2. 2025KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learningcited by 4
  3. 2024Stable and Safe Human-aligned Reinforcement Learning through Neural Ordinary Differential Equationscited by 3
  4. 2025Designing Robust Software Sensors for Nonlinear Systems via Neural Networks and Adaptive Sliding Mode Controlcited by 0
  5. 2026HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioningcited by 0
  6. 2026HyperKKL: Learning KKL Observers for Non-Autonomous Nonlinear Systems via Hypernetwork-Based Input Conditioningcited by 0
  7. 2026A KKL Observer Perspective on Reservoir Computingcited by 0