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 …
Interpolation, approximation and controllability of deep neural networks
We investigate the expressive power of deep residual neural networks idealized as
continuous dynamical systems through control theory. Specifically, we consider two …
continuous dynamical systems through control theory. Specifically, we consider two …
Near-optimal control of dynamical systems with neural ordinary differential equations
L Böttcher, T Asikis - Machine Learning: Science and Technology, 2022 - iopscience.iop.org
Near-optimal control of dynamical systems with neural ordinary differential equations -
IOPscience This site uses cookies. By continuing to use this site you agree to our use of cookies …
IOPscience This site uses cookies. By continuing to use this site you agree to our use of cookies …
Feature-informed data assimilation
We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In
FIDA, the information about feature events, such as shock waves, level curves, wavefronts …
FIDA, the information about feature events, such as shock waves, level curves, wavefronts …
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 …
Examples for separable control Lyapunov functions and their neural network approximation
In this paper, we consider nonlinear control systems and discuss the existence of a
separable control Lyapunov function. To this end, we assume that the system can be …
separable control Lyapunov function. To this end, we assume that the system can be …
Separable approximations of optimal value functions under a decaying sensitivity assumption
An efficient approach for the construction of separable approximations of optimal value
functions from interconnected optimal control problems is presented. The approach is based …
functions from interconnected optimal control problems is presented. The approach is based …
Deep neural network approximation of composite functions without the curse of dimensionality
A Riekert - arXiv preprint arXiv:2304.05790, 2023 - arxiv.org
In this article we identify a general class of high-dimensional continuous functions that can
be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) …
be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) …
A Directed Acyclic Graph Neural Network for AC Optimal Power Flow
AC optimal power flow (OPF) is of great significance for power system security, reliability,
and economy. As an NP-hard problem, its solution can be time consuming by traditional …
and economy. As an NP-hard problem, its solution can be time consuming by traditional …
Examples for existence and non-existence of separable control Lyapunov functions
L Grüne, M Sperl - 2022 - epub.uni-bayreuth.de
In this paper, we consider nonlinear control systems and discuss the existence of a
separable control Lyapunov function. To this end, we assume that the system can be …
separable control Lyapunov function. To this end, we assume that the system can be …