Can physics-informed neural networks beat the finite element method?
Partial differential equations play a fundamental role in the mathematical modelling of many
processes and systems in physical, biological and other sciences. To simulate such …
processes and systems in physical, biological and other sciences. To simulate such …
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 …
A neural network approach for high-dimensional optimal control applied to multiagent path finding
We propose a neural network (NN) approach that yields approximate solutions for high-
dimensional optimal control (OC) problems and demonstrate its effectiveness using …
dimensional optimal control (OC) problems and demonstrate its effectiveness using …
Learning optimal feedback operators and their sparse polynomial approximations
K Kunisch, D Vásquez-Varas, D Walter - Journal of Machine Learning …, 2023 - jmlr.org
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 …
Approximation of compositional functions with ReLU neural networks
The power of DNN has been successfully demonstrated on a wide variety of high-
dimensional problems that cannot be solved by conventional control design methods. These …
dimensional problems that cannot be solved by conventional control design methods. These …
A neural network approach applied to multi-agent optimal control
We propose a neural network approach for solving high-dimensional optimal control
problems. In particular, we focus on multi-agent control problems with obstacle and collision …
problems. In particular, we focus on multi-agent control problems with obstacle and collision …
Data-driven tensor train gradient cross approximation for hamilton–jacobi–bellman equations
A gradient-enhanced functional tensor train cross approximation method for the resolution of
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …
Gradient-augmented supervised learning of optimal feedback laws using state-dependent Riccati equations
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 …
problems is presented. A stabilizing feedback law is trained from a dataset generated from …
A neural network approach for stochastic optimal control
We present a neural network approach for approximating the value function of high-
dimensional stochastic control problems. Our training process simultaneously updates our …
dimensional stochastic control problems. Our training process simultaneously updates our …
Neural network optimal feedback control with guaranteed local stability
T Nakamura-Zimmerer, Q Gong… - IEEE Open Journal of …, 2022 - ieeexplore.ieee.org
Recent research shows that supervised learning can be an effective tool for designing near-
optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the …
optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the …