mlsanityData to 7 Oct 2026

Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems

arXiv 2210.01476 ↗First posted 4 Oct 2022math.OC cs.LG cs.SYcited by 11

Not on the map. Why?

Abstract (arXiv)

Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 11 of its 33 references that are in the map. First posted on arXiv 4 Oct 2022.

Builds on

11 of 33 references.

References · 11

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  3. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  4. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
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  8. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
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  10. 2018Generalization Error in Deep Learningcited by 46
  11. 2022Towards gain tuning for numerical KKL observerscited by 14

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 0; 2025: 3; 2026: 4.

11 papers.

  1. 2022Learning Robust State Observers using Neural ODEs (longer version)cited by 6
  2. 2025KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learningcited by 4
  3. 2023Sensor Fault Detection and Isolation in Autonomous Nonlinear Systems Using Neural Network-Based Observerscited by 1
  4. 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent Statescited by 1
  5. 2023Adaptive Meta-Learning-Based KKL Observer Design for Nonlinear Dynamical Systemscited by 1
  6. 2025PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systemscited by 1
  7. 2025Designing Robust Software Sensors for Nonlinear Systems via Neural Networks and Adaptive Sliding Mode Controlcited by 0
  8. 2026HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioningcited by 0
  9. 2026Verifiable Error Bounds for Physics-Informed Neural KKL Observerscited by 0
  10. 2026HyperKKL: Learning KKL Observers for Non-Autonomous Nonlinear Systems via Hypernetwork-Based Input Conditioningcited by 0
  11. 2026Correct then Forecast: Observer State-Space Models for Time Series Forecastingcited by 0