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 …

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 …

[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 …

External Optimal Control of the Semilinear Fractional Parabolic Coupled System

J Lei, W Wei - Journal of Optimization Theory and Applications, 2025 - Springer
This paper deals with an external optimal control problem governed by coupled system of
semilinear fractional parabolic equation and parabolic equation with Neumann exterior …

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 …

Optimal control for neural ODE in a long time horizon and applications to the classification and simultaneous controllability problems

JA Bárcena-Petisco - 2024 - hal.science
We study the optimal control in a long time horizon of neural ordinary differential equations
which are affine or whose activation function is homogeneous. When considering the …

[BOOK][B] Sensitivity Analysis and Goal Oriented Error Estimation for Model Predictive Control

M Schaller - 2021 - search.proquest.com
Gegenstand dieser Arbeit ist die Sensitivitätsanalyse und die spezialisierte adaptive
Diskretisierung für die modellprädiktive Regelung von Optimalsteuerungsproblemen mit …

[PDF][PDF] Almost periodic turnpike phenomenon for time-dependent systems

S Zamorano - cmc.deusto.eus
This paper explores the turnpike behavior of a controlled system with almost periodic inputs
and a cost functional based on almost periodic tracking term and periodic observation …

[PDF][PDF] Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation

H Antil, U Biccari, R Ponce, M Warma… - Evolution Equations and …, 2024 - par.nsf.gov
We study the controllability of trajectories, under positivity constraints on the control or the
state, of a one-dimensional heat equation involving the fractional Laplace operator (−∂ 2 x) …