Browsing by Author "Cerpa, Eduardo"

Now showing 1 - 8 of 8
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    A TRACKING PROBLEM FOR THE STATE OF CHARGE IN A ELECTROCHEMICAL LI-ION BATTERY MODEL
    (2022) Hernandez, Esteban; Prieur, Christophe; Cerpa, Eduardo
    In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.
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    Carleman estimates and controllability for a semi-discrete fourth-order parabolic equation
    (2022) Cerpa, Eduardo; Lecaros, Rodrigo; Nguyen, Thuy N. T.; Perez, Ariel
    The boundary controllability of fourth-order parabolic equations has been addressed in recent literature. However, there are no results concerning their numerical approximation and the behavior of discrete controls when the discretization parameter goes to zero. This paper is intended to cover this gap by studying this issue when the space operator is discretized and the time is kept as a continuous variable (semi-discrete approximation case). The proof is based on a relaxed observability inequality for the corresponding semi-discrete adjoint system and a suitable semi-discrete Carleman estimate.(c) 2022 Elsevier Masson SAS. All rights reserved.
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    Contributions to the singular perturbation theory of infinite-dimensional coupled systems
    (2025) Arias Neira, Gonzalo Andrés; Cerpa, Eduardo; Marx, Swann; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
    Singular perturbation and separation of time scales methods have been used to study the stability and control design for coupled ODE systems with different time scales for many years. This important literature was motivated by the fact that systems with significantly different time scales appear in several applications, in which the constituents of a coupled system may model different physical phenomena taking place in different time scales. The singular perturbation method (SPM), roughly speaking, aims to decouple a full system into two approximated subsystems based on a suitable time-scale separation. This thesis addresses problems concerning the stability, Tikhonov's approximation, stabilization, and control of singularly perturbed coupled infinite-dimensional systems.
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    OUTPUT FEEDBACK CONTROL OF A CASCADE SYSTEM OF LINEAR KORTEWEG-DE VRIES EQUATIONS
    (2021) Kitsos, Constantinos; Cerpa, Eduardo; Besancon, Gildas; Prieur, Christophe
    This paper is about the stabilization of a cascade system of n linear Korteweg-de Vries equations in a bounded interval. It considers an output feedback control placed at the left endpoint of the last equation, while the output involves only the solution to the first equation. The boundary control problems investigated include two cases: a classical control on the Dirichlet boundary condition and a less standard one on its second-order derivative. The feedback control law utilizes the estimated solutions of a high-gain observer system, and the output feedback control leads to stabilization for any n for the first boundary conditions case and for n = 2 for the second one.
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    Rapid exponential stabilization of a Boussinesq system of KdV-KdV Type
    (2023) Capistrano-Filho, Roberto de A.; Cerpa, Eduardo; Gallego, Fernando A.
    This paper studies the exponential stabilization of a Boussinesq system describing the two-way propagation of small amplitude gravity waves on the surface of an ideal fluid, the so-called Boussinesq system of the Korteweg-de Vries type. We use a Gramian-based method introduced by Urquiza to design our feedback control. By means of spectral analysis and Fourier expansion, we show that the solutions of the linearized system decay uniformly to zero when the feedback control is applied. The decay rate can be chosen as large as we want. The main novelty of our work is that we can exponentially stabilize this system of two coupled equations using only one scalar input.
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    Singular Perturbation Analysis for a Coupled KdV-ODE System
    (2024) Marx, Swann; Cerpa, Eduardo
    Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different time-scales appear. The singular perturbation method allows to decouple a full system into what are called the reduced-order system and the boundary layer system to get simpler stability conditions for the original system. In the infinite-dimensional setting, we do not have a general result making sure this strategy works. This article is devoted to this analysis for some systems coupling the Korteweg-de Vries equation and an ordinary differential equation with different time scales. More precisely, we obtain stability results and Tikhonov-type theorems.
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    Stability analysis of a linear system coupling wave and heat equations with different time scales
    (2025) Arias, Gonzalo; Cerpa, Eduardo; Marx, Swann
    In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of different time scales between the constituents of the system. This suggests the idea of applying a singular perturbation method to study stability properties. In fact, we prove that this method works for the system under study. Using this strategy, we get the stability of the system and a Tikhonov theorem, which allows us to approximate the solution of the coupled system using some appropriate uncoupled subsystems. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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    Towards a more accurate quasi-static approximation of the electric potential for neurostimulation with kilohertz-frequency sources
    (2023) Caussade, Thomas; Paduro, Esteban; Courdurier, Matias; Cerpa, Eduardo; Grill, Warren M.; Medina, Leonel E.
    Objective: Our goal was to determine the conditions for which a more precise calculation of the electric potential than the quasi-static approximation may be needed in models of electrical neurostimulation, particularly for signals with kilohertz-frequency components. Approach: We conducted a comprehensive quantitative study of the differences in nerve fiber activation and conduction block when using the quasi-static and Helmholtz approximations for the electric potential in a model of electrical neurostimulation. Main results: We first show that the potentials generated by sources of unbalanced pulses exhibit different transients as compared to those of energy-balanced pulses, and this is disregarded by the quasi-static assumption. Secondly, the relative errors for current-distance curves were below 3%, while for strength-duration curves the variations ranged between 1-17%, but could be improved to less than 3% across the range of pulse duration by providing a corrected quasi-static conductivity. Third, we extended our analysis to trains of pulses and reported a "congruence area" below 700 Hz, where the fidelity of fiber responses is maximal for supra-threshold stimulation. Further examination of waveforms and polarities revealed similar fidelities in the congruence area, but significant differences were observed beyond this area. However, the spike-train distance revealed differences in activation patterns when comparing the response generated by each model. Finally, in simulations of conduction-block, we found that block thresholds exhibited errors above 20% for repetition rates above 10 kHz. Yet, employing a corrected value of the conductivity improved the agreement between models, with errors no greater than 8%. Significance: Our results emphasize that the quasi-static approximation cannot be naively extended to electrical stimulation with high-frequency components, and notable differences can be observed in activation patterns. As well, we introduce a methodology to obtain more precise model responses using the quasi-static approach, which can be a valuable resource in computational neuroengineering.