Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEs
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Abstract (arXiv)
A procedure for the numerical approximation of high-dimensional Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed. Its main ingredients are a pseudospectral collocation approximation of the PDE dynamics, and an iterative method for the nonlinear HJB equation associated to the feedback synthesis. The latter is known as the Successive Galerkin Approximation. It can also be interpreted as Newton iteration for the HJB equation. At every step, the associated linear Generalized HJB equation is approximated via a separable polynomial approximation ansatz. Stabilizing feedback controls are obtained from solutions to the HJB equations for systems of dimension up to fourteen.
Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Feb 2017.
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Citing papers per year: 2021: 4; 2022: 2; 2023: 1; 2024: 2; 2025: 0; 2026: 1.
10 papers.
- 2022SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problemscited by 9
- 2021Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equationcited by 7
- 2021Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equationscited by 6
- 2021Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEscited by 5
- 2022Neural Network Optimal Feedback Control with Guaranteed Local Stabilitycited by 2
- 2023Actor-Critic Methods using Physics-Informed Neural Networks: Control of a 1D PDE Model for Fluid-Cooled Battery Packscited by 2
- 2024HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative modelscited by 2
- 2021Neural network optimal feedback control with enhanced closed loop stabilitycited by 1
- 2024Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEscited by 1
- 2026Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEscited by 0
- 2026Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs22 Jun 2026
- 2024HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models15 Sep 2024
- 2024Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs9 Sep 2024
- 2023Actor-Critic Methods using Physics-Informed Neural Networks: Control of a 1D PDE Model for Fluid-Cooled Battery Packs18 May 2023
- 2022Neural Network Optimal Feedback Control with Guaranteed Local Stability1 May 2022
- 2022SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems14 Jan 2022
- 2021Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation29 Dec 2021
- 2021Neural network optimal feedback control with enhanced closed loop stability15 Sep 2021
- 2021Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs7 May 2021
- 2021Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equations6 Mar 2021