mlsanityData to 7 Oct 2026

Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach

arXiv 2212.05259 ↗First posted 10 Dec 2022math.DS cs.LGcited by 3

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Abstract (arXiv)

Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: a) it allows for online real-time monitoring of a dynamical system; b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; c) it is computationally fast and less intensive than the popular Extended Dynamic Mode Decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 15 of its 31 references that are in the map. First posted on arXiv 10 Dec 2022.

Builds on

15 of 31 references.

References · 15

  1. 2021Next Generation Reservoir Computingcited by 160
  2. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  3. 2019Active Learning of Dynamics for Data-Driven Control Using Koopman Operatorscited by 31
  4. 2019Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Controlcited by 22
  5. 2018On Robust Computation of Koopman Operator and Prediction in Random Dynamical Systemscited by 8
  6. 2017Applied Koopman Operator Theory for Power Systems Technologycited by 7
  7. 2021Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysiscited by 5
  8. 2022Graph Neural Network and Koopman Models for Learning Networked Dynamics: A Comparative Study on Power Grid Transients Predictioncited by 5
  9. 2018Feedback Stabilization Using Koopman Operatorcited by 4
  10. 2020Model-Agnostic Algorithm for Real-Time Attack Identification in Power Grid using Koopman Modescited by 4
  11. 2018On Information Transfer Based Characterization of Power System Stabilitycited by 3
  12. 2019Data-Driven Operator Theoretic Methods for Global Phase Space Learningcited by 2
3 more
  1. 2020Data Driven Online Learning of Power System Dynamicscited by 2
  2. 2017Pulse-Based Control Using Koopman Operator Under Parametric Uncertaintycited by 1
  3. 2022Data-driven Stabilization of Discrete-time Control-affine Nonlinear Systems: A Koopman Operator Approachcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2026Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systemscited by 2
  2. 2024Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMDcited by 1
  3. 2025Conformal Online Learning of Deep Koopman Linear Embeddingscited by 0