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Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equations

arXiv 2103.04091 ↗First posted 6 Mar 2021math.OC cs.LG cs.SYcited by 6

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Abstract (arXiv)

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solves. The training phase is enriched by the use gradient information in the loss function, which is weighted through the use of hyperparameters. High-dimensional nonlinear stabilization tests demonstrate that real-time sequential large-scale Algebraic Riccati Equation solves can be substituted by a suitably trained feedforward neural network.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 14 of its 28 references that are in the map. First posted on arXiv 6 Mar 2021.

Builds on

14 of 28 references.

References · 14

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  2. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  3. 2019Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equationscited by 40
  4. 2016Algorithms for Overcoming the Curse of Dimensionality for Certain Hamilton-Jacobi Equations Arising in Control Theory and Elsewherecited by 21
  5. 2019Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architecturescited by 21
  6. 2016High-Dimensional Stochastic Optimal Control using Continuous Tensor Decompositionscited by 13
  7. 2015Mitigating the Curse of Dimensionality: Sparse Grid Characteristics Method for Optimal Feedback Control and HJB Equationscited by 12
  8. 2017Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEscited by 10
  9. 2020Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximationcited by 9
  10. 2014Linear Hamilton Jacobi Bellman Equations in High Dimensionscited by 8
  11. 2019A neural network based policy iteration algorithm with global H2-superlinear convergence for stochastic games on domainscited by 7
  12. 2017Algorithm for Overcoming the Curse of Dimensionality for State-dependent Hamilton-Jacobi equationscited by 6
2 more
  1. 2019Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equationscited by 5
  2. 2019Algorithms of Data Development For Deep Learning and Feedback Designcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 1; 2023: 0; 2024: 2; 2025: 0; 2026: 1.

6 papers.

  1. 2021Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEscited by 5
  2. 2022Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEscited by 3
  3. 2021Neural network optimal feedback control with enhanced closed loop stabilitycited by 1
  4. 2024Multi-level Optimal Control with Neural Surrogate Modelscited by 1
  5. 2024Data/moment-driven approaches for fast predictive control of collective dynamicscited by 0
  6. 2026Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEscited by 0