Learning continuous models for continuous physics
Dynamical systems that evolve continuously over time are ubiquitous throughout science
and engineering. Machine learning (ML) provides data-driven approaches to model and …
and engineering. Machine learning (ML) provides data-driven approaches to model and …
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 …
Leveraging multitime Hamilton–Jacobi PDEs for certain scientific machine learning problems
Hamilton–Jacobi partial differential equations (HJ PDEs) have deep connections with a wide
range of fields, including optimal control, differential games, and imaging sciences. By …
range of fields, including optimal control, differential games, and imaging sciences. By …
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 …
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 …
Feedforward neural networks and compositional functions with applications to dynamical systems
In this paper we develop an algebraic framework for analyzing neural network
approximation of compositional functions, a rich class of functions that are frequently …
approximation of compositional functions, a rich class of functions that are frequently …
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 …
Sympocnet: Solving optimal control problems with applications to high-dimensional multiagent path planning problems
Solving high-dimensional optimal control problems in real-time is an important but
challenging problem, with applications to multiagent path planning problems, which have …
challenging problem, with applications to multiagent path planning problems, which have …
Data-driven computational methods for the domain of attraction and Zubov's equation
This article deals with a special type of Lyapunov functions, namely the solution of Zubov's
equation. Such a function can be used to characterize the exact boundary of the domain of …
equation. Such a function can be used to characterize the exact boundary of the domain of …
Regulation of cost function weighting matrices in control of WMR using MLP neural networks
In this paper, a method based on neural networks for intelligently extracting weighting
matrices of the optimal controllers' cost function is presented. Despite the optimal and robust …
matrices of the optimal controllers' cost function is presented. Despite the optimal and robust …