Adaptive deep learning for high-dimensional Hamilton--Jacobi--Bellman equations
Computing optimal feedback controls for nonlinear systems generally requires solving
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …
Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures
We propose new and original mathematical connections between Hamilton–Jacobi (HJ)
partial differential equations (PDEs) with initial data and neural network architectures …
partial differential equations (PDEs) with initial data and neural network architectures …
Tensor decomposition methods for high-dimensional Hamilton--Jacobi--Bellman equations
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear
Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear …
Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear …
Using adaptive sparse grids to solve high‐dimensional dynamic models
We present a flexible and scalable method for computing global solutions of high‐
dimensional stochastic dynamic models. Within a time iteration or value function iteration …
dimensional stochastic dynamic models. Within a time iteration or value function iteration …
Polynomial approximation of high-dimensional Hamilton--Jacobi--Bellman equations and applications to feedback control of semilinear parabolic PDEs
A procedure for the numerical approximation of high-dimensional Hamilton--Jacobi--
Bellman (HJB) equations associated to optimal feedback control problems for semilinear …
Bellman (HJB) equations associated to optimal feedback control problems for semilinear …
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
We propose novel connections between several neural network architectures and viscosity
solutions of some Hamilton–Jacobi (HJ) partial differential equations (PDEs) whose …
solutions of some Hamilton–Jacobi (HJ) partial differential equations (PDEs) whose …
Learning optimal feedback operators and their sparse polynomial approximations
A learning based method for obtaining feedback laws for nonlinear optimal control problems
is proposed. The learning problem is posed such that the open loop value function is its …
is proposed. The learning problem is posed such that the open loop value function is its …
Optimal feedback law recovery by gradient-augmented sparse polynomial regression
A sparse regression approach for the computation of high-dimensional optimal feedback
laws arising in deterministic nonlinear control is proposed. The approach exploits the control …
laws arising in deterministic nonlinear control is proposed. The approach exploits the control …
QRnet: Optimal regulator design with LQR-augmented neural networks
In this letter we propose a new computational method for designing optimal regulators for
high-dimensional nonlinear systems. The proposed approach leverages physics-informed …
high-dimensional nonlinear systems. The proposed approach leverages physics-informed …
Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations
We address finding the semi-global solutions to optimal feedback control and the Hamilton–
Jacobi–Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal …
Jacobi–Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal …