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 …
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
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 …
optimality conditions of nonlinear optimal control problems with respect to perturbations of …
[PDF][PDF] Averaged turnpike property for differential equations with random constant coefficients
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 …
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 …
semilinear fractional parabolic equation and parabolic equation with Neumann exterior …
Uniform Turnpike Property and Singular Limits
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 …
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 …
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 …
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 …
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
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) …
state, of a one-dimensional heat equation involving the fractional Laplace operator (−∂ 2 x) …