mlsanityData to 7 Oct 2026

Kernel-Based Optimal Control: An Infinitesimal Generator Approach

arXiv 2412.01591 ↗First posted 2 Dec 2024math.OC cs.LG cs.ROcited by 1

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Abstract (arXiv)

This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 23 of its 59 references that are in the map. First posted on arXiv 2 Dec 2024.

Builds on

23 of 59 references.

References · 23

  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2019Data-driven approximation of the Koopman generator: Model reduction, system identification, and controlcited by 85
  3. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  4. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  5. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
  6. 2023Sharp Spectral Rates for Koopman Operator Learningcited by 35
  7. 2022Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problemcited by 27
  8. 2021Finite-data error bounds for Koopman-based prediction and controlcited by 26
  9. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 23
  10. 2023Koopman Kernel Regressioncited by 22
  11. 2020Nonparametric approximation of conditional expectation operatorscited by 21
  12. 2024Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verificationcited by 12
11 more
  1. 2023Consistent Long-Term Forecasting of Ergodic Dynamical Systemscited by 10
  2. 2024Learning the Infinitesimal Generator of Stochastic Diffusion Processescited by 9
  3. 2019HJB Optimal Feedback Control with Deep Differential Value Functions and Action Constraintscited by 8
  4. 2024Nonparametric Control Koopman Operatorscited by 7
  5. 2021Continuous-Time Fitted Value Iteration for Robust Policiescited by 6
  6. 2022Data-Driven Chance Constrained Control using Kernel Distribution Embeddingscited by 5
  7. 2020Towards Global Optimal Control via Koopman Liftscited by 3
  8. 2023Convex operator-theoretic methods in stochastic controlcited by 3
  9. 2018Solving Chance Constrained Optimization under Non-Parametric Uncertainty Through Hilbert Space Embeddingcited by 2
  10. 2023Controlled density transport using Perron Frobenius generatorscited by 2
  11. 2024Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spacescited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Koopman operator theory: fundamentals, control, and applicationscited by 1