Deep Neural Network Approximations for the Stable Manifolds of the Hamilton–Jacobi–Bellman Equations

Chen, Guoyuan

doi:10.1109/tac.2024.3396107

IEEE Trans. Automat. Contr.

2024

DOI: 10.1109/tac.2024.3396107

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Deep Neural Network Approximations for the Stable Manifolds of the Hamilton–Jacobi–Bellman Equations

Guoyuan Chen

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Regularization and Propagation in a Hamilton–Jacobi–Bellman-Type Equation in Infinite-Dimensional Hilbert Space

Bianca,

Dogbe

2024

Symmetry

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This paper is devoted to new propagation and regularity results for a class of first-order Hamilton–Jacobi–Bellman-type problems in a separable infinite-dimensional Hilbert space. Specifically, the related Cauchy problem is investigated by employing the Faedo–Galerkin approximation method. Under some structural assumptions, the main result is obtained by using the probabilistic representation formula of the solution in order to define the weak continuity assumptions, by assuming the existence of a symmetric positive definite Hilbert–Schmidt operator and by employing modulus continuity arguments.

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Regularization and Propagation in a Hamilton–Jacobi–Bellman-Type Equation in Infinite-Dimensional Hilbert Space

Bianca,

Dogbe

2024

Symmetry

View full text Add to dashboard Cite

show abstract

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Deep Neural Network Approximations for the Stable Manifolds of the Hamilton–Jacobi–Bellman Equations

Cited by 1 publication

References 36 publications

Regularization and Propagation in a Hamilton–Jacobi–Bellman-Type Equation in Infinite-Dimensional Hilbert Space

Regularization and Propagation in a Hamilton–Jacobi–Bellman-Type Equation in Infinite-Dimensional Hilbert Space

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