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 …

Large time control and turnpike properties for wave equations

E Zuazua - Annual Reviews in Control, 2017 - Elsevier
In the last decades mathematical control theory has been extensively developed to handle
various models, including Ordinary and Partial Differential Equations (ODE and PDE), both …

Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs

L Grüne, M Schaller, A Schiela - ESAIM: Control, Optimisation and …, 2021 - esaim-cocv.org
We analyze the sensitivity of the extremal equations that arise from the first order necessary
optimality conditions of nonlinear optimal control problems with respect to perturbations of …

The turnpike property in semilinear control

D Pighin - ESAIM: Control, Optimisation and Calculus of …, 2021 - esaim-cocv.org
An exponential turnpike property for a semilinear control problem is proved. The state-target
is assumed to be small, whereas the initial datum can be arbitrary. Turnpike results are also …

[PDF][PDF] Turnpike in lipschitz-nonlinear optimal control

C Esteve, B Geshkovski, D Pighin… - arxiv preprint arxiv …, 2020 - hal.science
We present a new proof of the turnpike property for nonlinear optimal control problems,
when the running target is a steady control-state pair of the underlying dynamics. Our …

[HTML][HTML] Control in moving interfaces and deep learning

B Geshkovski - 2021 - dialnet.unirioja.es
Control in moving interfaces and deep learning - Dialnet Ayuda ¿En qué podemos ayudarle?
× Buscar en la ayuda Buscar Consultar la ayuda ¿En qué podemos ayudarle? × Buscar en la …

Turnpike in Lipschitz—nonlinear optimal control

C Esteve-Yagüe, B Geshkovski, D Pighin… - Nonlinearity, 2022 - iopscience.iop.org
We present a new proof of the turnpike property for nonlinear optimal control problems,
when the running target is a steady control-state pair of the underlying system. Our strategy …

[PDF][PDF] Averaged turnpike property for differential equations with random constant coefficients

M Hernandez, R Lecaros, S Zamorano - 2023 - opus4.kobv.de
This paper studies the integral turnpike and turnpike in average for a class of random or-
dinary differential equations. We prove that, under suitable assumptions on the matrices that …

Exponential turnpike property for fractional parabolic equations with non-zero exterior data

M Warma, S Zamorano - ESAIM: Control, Optimisation and Calculus …, 2021 - esaim-cocv.org
We consider averages convergence as the time-horizon goes to infinity of optimal solutions
of time-dependent optimal control problems to optimal solutions of the corresponding …

Uniform Turnpike Property and Singular Limits

M Hernández, E Zuazua - Acta Applicandae Mathematicae, 2024 - Springer
Motivated by singular limits for long-time optimal control problems, we investigate a class of
parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with …