Turnpike properties in optimal control: An overview of discrete-time and continuous-time results

T Faulwasser, L Grüne - Handbook of numerical analysis, 2022 - Elsevier
The turnpike property refers to the phenomenon that in many optimal control problems, the
solutions for different initial conditions and varying horizons approach a neighborhood of a …

Neural ODE control for classification, approximation, and transport

D Ruiz-Balet, E Zuazua - SIAM Review, 2023 - SIAM
We analyze neural ordinary differential equations (NODEs) from a control theoretical
perspective to address some of the main properties and paradigms of deep learning (DL), in …

Turnpike in optimal control of PDEs, ResNets, and beyond

B Geshkovski, E Zuazua - Acta Numerica, 2022 - cambridge.org
The turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …

Turnpike properties in optimal control: An overview of discrete-time and continuous-time results

T Faulwasser, L Grüne - ar**s with a view to the deep learning
A Agrachev, A Sarychev - Journal of Dynamical and Control Systems, 2022 - Springer
Deep learning of the artificial neural networks (ANN) can be treated as a particular class of
interpolation problems. The goal is to find a neural network whose input-output map …

Interpolation and approximation via momentum resnets and neural odes

D Ruiz-Balet, E Affili, E Zuazua - Systems & Control Letters, 2022 - Elsevier
In this article, we explore the effects of memory terms in continuous-layer Deep Residual
Networks by studying Neural ODEs (NODEs). We investigate two types of models. On one …