Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton–Jacobi PDEs
Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi
PDEs are important but challenging problems in control engineering. In this paper, we …
PDEs are important but challenging problems in control engineering. In this paper, we …
A non-gradient method for solving elliptic partial differential equations with deep neural networks
Y Peng, D Hu, ZQJ Xu - Journal of Computational Physics, 2023 - Elsevier
Deep learning has achieved wide success in solving Partial Differential Equations (PDEs),
with particular strength in handling high dimensional problems and parametric problems …
with particular strength in handling high dimensional problems and parametric problems …
Neural network optimal feedback control with enhanced closed loop stability
T Nakamura-Zimmerer, Q Gong… - 2022 American Control …, 2022 - ieeexplore.ieee.org
Recent research has shown that supervised learning can be an effective tool for designing
optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the …
optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the …
Initial value problem enhanced sampling for closed-loop optimal control design with deep neural networks
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-
standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi …
standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi …
Lax-Oleinik-type formulas and efficient algorithms for certain high-dimensional optimal control problems
Two of the main challenges in optimal control are solving problems with state-dependent
running costs and developing efficient numerical solvers that are computationally tractable …
running costs and developing efficient numerical solvers that are computationally tractable …
Developing Explainable Deep Model for Discovering Novel Control Mechanism of Neuro-Dynamics
Human brain is a complex system composed of many components that interact with each
other. A well-designed computational model, usually in the format of partial differential …
other. A well-designed computational model, usually in the format of partial differential …
[HTML][HTML] Optimal polynomial feedback laws for finite horizon control problems
K Kunisch, D Vásquez-Varas - Computers & Mathematics with Applications, 2023 - Elsevier
A learning technique for finite horizon optimal control problems and its approximation based
on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is …
on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is …
Hopf-type representation formulas and efficient algorithms for certain high-dimensional optimal control problems
Two key challenges in optimal control include efficiently solving high-dimensional problems
and handling optimal control problems with state-dependent running costs. In this paper, we …
and handling optimal control problems with state-dependent running costs. In this paper, we …
Learning optimal feedback operators and their polynomial approximation
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 …
Empowering optimal control with machine learning: A perspective from model predictive control
Solving complex optimal control problems have confronted computational challenges for a
long time. Recent advances in machine learning have provided us with new opportunities to …
long time. Recent advances in machine learning have provided us with new opportunities to …