arXiv subjects

Sebastián Zamorano

Publications and source records attributed to Sebastián Zamorano.

6 recordsLinked to original sources

arXiv2026

Tracking controllability for finite-dimensional linear systems

This paper develops a functional-analytic characterization of output tracking controllability for finite-dimensional linear systems. By formulating tracking as the surjectivity of the control-to-output map on suitable trajectory spaces, we show that exact tracking is equivalent to a trajectory-space observability inequality associated with the dual input-output structure. This characterization enables a Hilbert Uniqueness Method (HUM) type variational construction of minimum-norm tracking controls and makes explicit the intrinsic regularity requirements on reference trajectories induced by the system dynamics and the output operator. The same framework also yields a natural notion of approximate tracking when exact tracking fails. We provide explicit formulas in the scalar case and report illustrative numerical examples for ODEs and semi-discretized PDEs, demonstrating the method for both smooth and nonsmooth targets.

math.OC↗

arXiv2025

A control-based spatial source reconstruction in fractional heat equations

This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state and its time derivative over a subset of the domain. A reconstruction formula for the Fourier coefficients of the unknown source is derived, leveraging the null controllability property of the fractional heat equation when the fractional order lies in the interval $s\in(1/2,1)$. The methodology builds on spectral analysis and Volterra integral equations, providing a robust framework for recovering spatial sources under limited measurement data. Numerical experiments confirm the accuracy and stability of the proposed approach.

math.NA↗

arXiv2024

Averaged observations and turnpike phenomenon for parameter-dependent systems

Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions with respect to the matrices that defined the dynamics and the cost functional, we prove that the optimal control and state for the evolutionary problem converge in average to the optimal pair of an associated stationary problem. Moreover, we characterize the closeness between these two optimal solutions, proving that over a large time interval, they are exponentially close.

math.OC↗

arXiv2022

Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions

We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding adjoint system. This is done by using a suitable Carleman estimate for such models where the discrete parameters $h$ and $Δt$ are connected to the one of the large Carleman parameters.

math.AP↗

arXiv2021

An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz stability for this inverse problem, and we design a convergent algorithm for the reconstruction of the unknown coefficient. The techniques used are based on Carleman inequalities for wave equations and properties of the MGT equation.

math.AP↗

arXiv2019

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

We study the controllability to trajectories, under positivity constraints on the control or the state, of a one-dimensional heat equation involving the fractional Laplace operator $ (-\partial_x^2)^s$ (with $0<s<1$) on the interval $(-1,1)$. Our control function is localized in an open set $\mathcal O$ in the exterior of $(-1,1)$, that is, $\mathcal O\subset (\mathbb{R} \setminus (-1,1))$. We show that there exists a minimal (strictly positive) time $T_{\rm min}$ such that the fractional heat dynamics can be controlled from any initial datum in $L^2(-1,1)$ to a positive trajectory through the action of an exterior positive control, if and only if $\frac 12<s<1$. In addition, we prove that at this minimal controllability time, the constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. Finally, we provide several numerical illustrations that confirm our theoretical results.

math.OC↗