Carlos Esteve Yagüe

Carlos Esteve Yagüe
Universidad Autónoma de Madrid | UAM · Department of Mathematics

About

20
Publications
2,076
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
49
Citations

Publications

Publications (20)
Article
Full-text available
We analyze the consequences that the so-called turnpike property has on the longtime behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained controls. We prove that, when the time horizon T tends to infinity, the value function asymptotically behaves as...
Article
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 combines the construction of quasi-turnpike controls via controllability, and a bootstrap argument, and does not rely on analyzing the optimality system or linearizatio...
Preprint
Full-text available
We give a full characterization of the range of the operator which associates, to any initial condition, the viscosity solution at time $T$ of a Hamilton-Jacobi equation with convex Hamiltonian. Our main motivation is to be able to treat the case of convex Hamiltonians with no further regularity assumptions. We give special attention to the case $H...
Preprint
Full-text available
We consider the Selective Harmonic Modulation (SHM) problem, consisting in the design of a staircase control signal with some prescribed frequency components. In this work, we propose a novel methodology to address SHM as an optimal control problem in which the admissible controls are piecewise constant functions, taking values only in a given fini...
Preprint
Full-text available
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 under- lying dynamics. Our strategy combines the construction of suboptimal quasi-turnpike trajectories via controllability, and a bootstrap argument, and does not rely on an- alyzing the optimality s...
Preprint
Full-text available
In this article, we the optimal control and neural ordinary differential equation (neural ODE) perspective of deep supervised learning. Our objective is, via rigorous analysis, to study the impact of the final time horizon T appearing in the neural ODE, on the training error and the optimal parameters.
Preprint
Full-text available
It is by now well-known that practical deep supervised learning may roughly be cast as an optimal control problem for a specific discrete-time, nonlinear dynamical system called an artificial neural network. In this work, we consider the continuous-time formulation of the deep supervised learning problem, and study the latter's behavior when the fi...
Preprint
In this work, we analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to an optimal control problem. As a by-product, we obtain the long-time behavior of the solution to the associated Hamilton-Jacobi-Bellman equation. In order to carry out our study, we use the setting of a...
Preprint
Full-text available
We study the inverse problem, or inverse design problem, for a time-evolution Hamilton-Jacobi equation. More precisely, given a target function $u_T$ and a time horizon $T>0$, we aim to construct all the initial conditions for which the viscosity solution coincides with $u_T$ at time $T$. As it is common in this kind of nonlinear equations, the tar...
Thesis
Full-text available
This thesis is concerned with the study of three nonlinear parabolic problems : We start with a mathematical model for a micro-electro-mechanical system (MEMS) with variable dielectric permittivity. The model is based on a parabolic equation with singular nonlinearity which describes the dynamic deffection of an elastic plate under the effect of an...
Preprint
We consider the diffusive Hamilton-Jacobi equation $u_t - \Delta u = |\nabla u|^p$ in a bounded planar domain with zero Dirichlet boundary condition. It is known that, for $p>2$, the solutions to this problem can exhibit gradient blow-up (GBU) at the boundary. In this paper we study the possibility of the GBU set being reduced to a single point. In...
Preprint
Full-text available
In this paper we study the evolution problem u_t(x, t) − λ_j (D^2 u(x, t)) = 0, in Ω × (0, +∞), u(x, t) = g(x, t), on ∂Ω × (0, +∞), u(x, 0) = u_0 (x), in Ω, where Ω is a bounded domain in R^N (that verifies a suitable geometric condition on its boundary) and \lambda_j (D^2 u) stands for the j−st eigenvalue of the Hessian matrix D^2 u. We assume tha...
Article
Full-text available
We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, based on a parabolic equation with singular nonlinearity. We study the touchdown or quenching phenomenon. Recently, the question whether or not touchdown can occur at zero points of the permittivity profile f, which had long remained ope...
Article
Full-text available
We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, involving a parabolic equation with singular nonlinearity. We study the touchdown, or quenching, phenomenon. Recently, the question whether or not touchdown can occur at zero points of the premittivity profile f, which had long remained...
Article
Full-text available
We obtain upper bounds for the decay rate for solutions to the nonlocal problem ∂tu(x,t)=∫RnJ(x,y)|u(y,t)−u(x,t)|p−2(u(y,t)−u(x,t))dy with an initial condition u0∈L1(Rn)∩L∞(Rn) and a fixed p>2. We assume that the kernel J is symmetric, bounded (and therefore there is no regularizing effect) but with polynomial tails, that is, we assume a lower boun...