Publications – cmc.deusto.eus

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

H. Antil, U. Biccari, R. Ponce, M. Warma, S. Zamorano (2024) Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation, Vol. 13, pp. 893-924, https://doi.org/10.3934/eect.2024010…

Boundary Controllability for the 1D Moore-Gibson-Thompson equation

C. Lizama, S. Zamorano (2023) Boundary Controllability for the 1D Moore-Gibson-Thompson equation, Meccanica 58, Vol. 58, pp. 1031-1038, 10.1007/s11012-022-01551-3. https://link.springer.com/article/10.1007/s11012-022-01551-3 Abstract. This article addresses the boundary controllability problem for a…

Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields

M. Hernández, R. Lecaros, S. Zamorano (2023) Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields , Vol. 365, pp. 808-832, https://www.aimsciences.org/article/doi/10.3934/mcrf.2022016 Abstract. This…

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

R. Lecaros, R. Morales, A. Pérez, S. Zamorano (2023) Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions, Differ. Equ., Vol. 365, pp.…

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

R. Arancibia, R. Lecaros, A. Mercado, S. Zamorano (2022) An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound, J. Inverse Ill-Posed Probl., Vol. 30, No. 5, pp. 659-675,…

Averaged observations and turnpike phenomenon for parameter-dependent systems

M. Hernandez, M. Lazar, S. Zamorano (2024) Averaged observations and turnpike phenomenon for parameter-dependent systems arXiv:2404.17455 Abstract. Our main contribution in this article is the achievement of the turnpike property…

Almost periodic turnpike phenomenon for time-dependent systems

S. Zamorano (2024)Almost periodic turnpike phenomenon for time-dependent systems Abstract. This paper explores the turnpike behavior of a controlled system with almost periodic inputs and a cost functional based on…

Tracking controllability for finite-dimensional linear systems

S. Zamorano, E. Zuazua (2024)Tracking controllability for finite-dimensional linear systems arXiv:2407.18641v1 Abstract. We introduce and analyze the concept of tracking controllability, where the objective is for the state of a…

Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications

Z. Li, K. Liu, L. Liverani, E. Zuazua (2024)Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications arXiv:2407.17092 Abstract. In this paper, we introduce semi-autonomous neural ordinary differential…

Deep Neural Networks: Multi-Classification and Universal Approximation

M. Hernández, E. Zuazua (2023)Approximate and Weighted Data Reconstruction Attack in Federated Learning arXiv:2409.06555 Abstract. We demonstrate that a ReLU deep neural network with a width of 2 and a…

Optimized classification with neural odes via separability

A. Alvarez-Lopez, R. Orive-Illera, E. Zuazua (2024)Optimized classification with neural odes via separability Neural Networks, Vol. 180, 106640, arXiv:2312.13807 Abstract. Classification of N points becomes a simultaneous control problem when…

Approximate and Weighted Data Reconstruction Attack in Federated Learning

E. Wang E, Y. Song, E. Zuazua (2023)Approximate and Weighted Data Reconstruction Attack in Federated Learning arXiv:2308.06822 Abstract. Federated Learning (FL) is a distributed learning paradigm that enables multiple clients…

Random Batch Method (RBM) and Model Predictive Control (MPC) for Converter-Dominated Power Systems

C. Vázquez. Random Batch Method (RBM) and Model Predictive Control (MPC) for Converter-Dominated Power Systems (2024) Abstract. This paper investigates the application of Data-based Reduced Order Models, the Random Batch…

Interplay between depth and width for interpolation in neural ODEs

A. Alvarez-Lopez, A. Hadj Slimane, E. Zuazua. Interplay between depth and width for interpolation in neural ODEs (2024) M3AS Abstract. Neural ordinary differential equations (neural ODEs) have emerged as a…

Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings

GM. Coclite, N. De Nitti, F. Maddalena, G. Orlando, E. Zuazua. Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings (2024) M3AS Abstract. We study…

FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning

E. Zuazua. FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning (2024) https://doi.org/10.48550/arXiv.2402.13989 Abstract. Federated learning (FL) is a promising framework for learning from distributed data while maintaining privacy. The…

Fourier series and sidewise control of 1-d waves

E. Zuazua. Fourier series and sidewise control of 1-d waves (2024) Volume in honor of Yves Meyer, Documents Mathématiques of the French Mathematical Society (SMF), Vol. 22, p. 341-365, arXiv:2308.04906…

Uniform Turnpike Property and Singular Limits

M Hernandez-Salinas, E. Zuazua. Uniform Turnpike Property and Singular Limits (2024) Springer Verlag, Vol. 190, No. 3, https://doi.org/10.1007/s10440-024-00640-7 Abstract. Motivados por límites singulares para problemas de control óptimo a largo…

Pointwise constraints for scalar conservation laws with positive wave velocity

N. De Nitti, D. Serre, E. Zuazua. Pointwise constraints for scalar conservation laws with positive wave velocity (2024) Abstract. We consider a conservation law with strictly positive wave velocity and…

Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system

T. Crin-Barat, E. Zuazua. Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: Application to the nonlinearly damped p-system (2024) Ann. Inst. Henri Poincare (C) Anal. Non Lineaire,…

Tracking controllability for the heat equation

J.A. Barcena-Petisco, E. Zuazua. Tracking controllability for the heat equation (2024) Abstract. We study the tracking or sidewise control- lability of the heat equation. More precisely, we seek for controls…

Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements

J. Lecarós, J. Lopez-Rios, G.I. Montecinos, E. Zuazua. Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements, (2024) Math. Meth. Appl. Sci., pp. 1–32, https://doi.org/10.1002/mma.10251…

Exact Controllability and Stabilization of the Wave Equation

E. Zuazua. Exact Controllability and Stabilization of the Wave Equation (2024) UNITEXT - Springer Abstract. These Notes originated from a course I delivered at the Institute of Mathematics of the…

Stability and Convergence of a Randomized Model Predictive Control Strategy

Daniël Veldman, Alexandra Borkowski, Enrique Zuazua. Stability and Convergence of a Randomized Model Predictive Control Strategy (2024) IEEE Trans. Automat., Vol. 69, No. 9, pp. 6253-6260 Abstract. This paper is concerned…

Control of neural transport for normalizing flows

D. Ruiz-Balet, E. Zuazua. Control of neural transport for normalizing flows (2023) J. Math. Pures Appl. https://doi.org/10.48550/arXiv.2307.07817 Abstract. Inspired by normalizing flows, we analyze the bilinear control of neural transport…

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

U. Biccari, Y. Song, X. Yuan, E. Zuazua. A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation (2023) Inverse Problems, IP-103963, https://arxiv.org/abs/2202.01589 Abstract. We consider…

Gaussian Beam ansatz for finite difference wave equations

Biccari U, Zuazua E. Gaussian Beam ansatz for finite difference wave equations (2023) Abstract. This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation…

Optimal design of sensors via geometric criteria

I. Ftouhi, Zuazua E.. Optimal design of sensors via geometric criteria (2023) J. Geom. Anal., Vol. 33, No. 253, https://doi.org/10.1007/s12220-023-01301-1 Abstract. We consider a convex set Ω and look for…

Eigenvalue bounds for the Gramian operator of the heat equation

M. Lazar, Zuazua E.. Eigenvalue bounds for the Gramian operator of the heat equation (2024) Automatica, Vol. 164, pp. 111-653, https://doi.org/10.1016/j.automatica.2024.111653 Abstract. This paper is concerned with the eigenvalue decay…

Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave

G.M. Coclite, De Nitti N., Zuazua E.. Long-time convergence of a nonlocal Burgers' equation towards the local N-wave (2023) CVGMT Abstract. We study the long-time behavior of the unique weak…

On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov methods

N. Nitti, De Nitti N., Zuazua E.. On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov methods (2023) Vietnam J. Math. https://doi.org/10.1007/s10013-022-00598-9 Abstract. In…

Optimal actuator design via Brunovsky’s normal form

Brunovsky normal form, Controllability, finite-dimensional systems, Kalman rank condition, lumped control, optimal actuator design.

B. Geshkovski, E. Zuazua, Optimal actuator design via Brunovsky's normal form (2022) IEEE Automatic Control, Vol. 26, No. 12, DOI: 10.1109/TAC.2022.3181222 Abstract: In this paper, by using the Brunovsky normal…

Control of certain parabolic models from biology and social sciences

Domènec Ruiz-Balet, , Enrique Zuazua. Control of certain parabolic models from biology and social sciences(2022) Math Control and Related Fields, Vol. 12, No. 4, pp 955-1038. doi: https://doi.org/10.3934/mcrf.2022032 Abstract. These…

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation

R. Bianchini, Crin-Barat T., M. Paicu. Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation (2022) Abstract. We prove the nonlinear asymptotic stability of stably stratified solutions…

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Esteve C., Zuazua E.. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws (2022) Nonlinear Analysis, Vol. 227, https://doi.org/10.1016/j.na.2022.113167 Abstract. We give a full characterization of the…

Spectral inequalities for elliptic pseudo-differential operators on closed manifolds

D. Cardona. Spectral inequalities for elliptic pseudo-differential operators on closed manifolds (2022) Abstract. Let be a closed Riemannian manifold. The aim of this work is to prove the Lebeau-Robbiano spectral…

Control and Machine Learning

Zuazua E. Control and Machine Learning (2022) News journal of the Society for Industrial and Applied Mathematics , Vol. 55, No. 8 Abstract. There are two recurring questions arising when…

Greedy algorithm for parameter dependent operator Lyapunov equations

Martin Lazar, Jerome Weston. Greedy algorithm for parameter dependent operator Lyapunov equations (2021) Systems & Control Letters, Vol. 154, pp. 104968. Abstract. The aim of this paper is to provide…

Optimal distributed control of linear parabolic equations by spectral decomposition

Martin Lazar, Cesare Molinari. Optimal distributed control of linear parabolic equations by spectral decomposition (2021) Optimal Control Applications and Methods, Vol. 42, No. 4, pp. 891-926. Abstract. We construct an…

Null controllability of a nonlinear age, space and two-sex structured population dynamics model

Yacouba Simporé, Oumar Traoré. Null controllability of a nonlinear age, space and two-sex structured population dynamics model (2021) Mathematical Control and Related Fields Abstract. In this paper, we study the…

Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System

Crin-Barat T., L. Shou. Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System (2022) Abstract. In this paper we study the diffusive relaxation limit of the Jin-Xin system toward viscous…

Neural ODE Control for Classification, Approximation and Transport

data classification, deep learning, Neural ODEs, Optimal Transport, simultaneous control, transport equations, universal approximation, Wasserstein distance

Ruiz-Balet D., Zuazua E. Neural ODE Control for Classification, Approximation and Transport (2023), SIAM Review, Vol. 65, No. 3, pp. 735-773, https://doi.org/10.1137/21M1411433 Abstract. We analyze Neural Ordinary Differential Equations (NODEs)…

Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion

Yacouba Simporé, Umberto Biccari. Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion (2022) Abstract. In this article, we consider the infinite dimensional linear control system…

Null Controllability for a Degenerate Structured Population Model

Yacouba Simporé, Yassine El gantouh, Umberto Biccari. Null Controllability for a Degenerate Structured Population Model (2022) Abstract. In this paper, we consider the infinite dimensional linear control system describing population…

Greedy search of optimal approximate solutions

M. Lazar, E. Zuazua. Greedy search of optimal approximate solutions (2022) Commun. Optim. Theory Abstract. In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed…

Control of reaction-diffusion models in biology and social sciences

comparison principle, Constraints, Control, Mathematical biology, paths of steady-states, phase plane, Reaction-diffusion, traveling waves

Domènec Ruiz-Balet, Enrique Zuazua. Control of reaction-diffusion models in biology and social sciences (2022) Math. Control Relat. Fields Abstract. These lecture notes address the controllability under state constraints of reaction-diffusion equations…

Turnpike in Optimal Control PDES, ResNets, and beyond

Brunovsky normal form, Controllability, finite-dimensional systems, Kalman rank condition, lumped control, optimal actuator design.

B. Geshkovski, E. Zuazua, Turnpike in Optimal Control PDES, ResNets and beyond (2022) Acta Numer., Vol. 31, pp. 135-263. doi:10.1017/S0962492922000046 Abstract: The turnpike property in contemporary macroeconomics asserts that if…

Local Stability and Convergence of Unconstrained Model Predictive Control

Daniël Veldman, Enrique Zuazua. Local Stability and Convergence of Unconstrained Model Predictive Control (2022) Abstract. The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based on…

Preface- Control and Analysis of Partial Differential Equations

Nicolae Cîndea, Günter Leugering, Jëróme Lohêac, Sorin Micu, Kirsten Morris, Takeo Takahashi and Enrique Zuazua. Preface- Control and Analysis of Partial Differential Equations, Marius Tucsbak 60th Anniversary Volume (2022) Math.…

On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

Crin-Barat T., De Nitti N., Zuazua E.. On the decay of one-dimensional locally and partially dissipated and hyperbolic systems (2022) Abstract. We study the time-asymptotic behavior of linear hyperbolic systems…

A framework for randomized time-splitting in linear-quadratic optimal control

Daniël Veldman, Enrique Zuazua. (2022)A framework for randomized time-splitting in linear-quadratic optimal control Numerische Mathematik. DOI: https://doi.org/10.1007/s00211-022-01290-3 Abstract. Inspired by the successes of stochastic algorithms in the training of deep neural…

Nonuniqueness of minimizers for semilinear optimal control problems

D. Pighin. Nonuniqueness of minimizers for semilinear optimal control problems (2022) J. Eur. Math. Soc, , published online first. https://doi.org/10.4171/jems/1232 Abstract. A counterexample to uniqueness of global minimizers of semilinear…

The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

C. Esteve, H. Kouhkouh, D. Pighin, E. Zuazua. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems. Math. Control Signals Syst. (2022). https://doi.org/10.1007/s00498-022-00325-2 Abstract:…

Numerical Control: Part A

Emmanuel Trélat, Enrique Zuazua. Numerical Control: Part A First Edition (2022), Elsevier Science & Technology. Handbook of Numerical Analysis XXIII, Vol. 23, p. 1-558, eBook ISBN: 9780323853392, Hardcover ISBN: 9780323850599…

Interpolation and approximation via Momentum ResNets and Neural ODEs

Domènec Ruiz-Balet, Elisa Affili , Enrique Zuazua. Interpolation and approximation via Momentum ResNets and Neural ODEs IEEE Control Syst. Lett. (2022) Vol. 162, ISSN 0167-6911, https://doi.org/10.1016/j.sysconle.2022.105182 Abstract. In this article,…

Linear projection-based CEST parameter estimation

F. Glang, Moritz Fabian, A. German, Katrin M Khakzar, A. Mennecke, A. Liebert, K. Herz, P. Liebig, B. Kasper, Manuel Schmidt, E. Zuazua, A. Nagel, F. Laun, A. Dörfler, K.…

Turnpike in Lipschitz-nonlinear optimal control

Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control Nonlinearity. Vol 5. No. 34, pp. 1652-1701 (2022) https://doi.org/10.1088/1361-6544/ac4e61 Abstract. We present a new proof of…

The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term

Shi Jin, Yuhua Zhu, Enrique Zuazua. The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term Numer. Math. 150, 479–519 (2022). https://doi.org/10.1007/s00211-021-01257-w Abstract. We consider the Vlasov-Fokker-Planck equation with random electric…

Analysis and numerical solvability of backward-forward conservation laws

Thibault Liard, Enrique Zuazua. Analysis and numerical solvability of backward-forward conservation laws (2022) SIAM Journal on Mathematical Analysis Abstract. In this paper, we study the problem of initial data identification…

Control and Numerical approximation of Fractional Diffusion Equations

Exterior Control, Finite Element Method, Fractional diffusion equation, Fractional Laplacian, Interior Control, Numerical approximation, simultaneous control

Umberto Biccari, Mahamadi Warma, Enrique Zuazua. Control and Numerical approximation of Fractional Diffusion Equations (2022) Handb. Numer. Anal. Elsevier. ISSN:1570-8659, DOI: https://doi.org/10.1016/bs.hna.2021.12.001 Abstract. The aim of this work is to give…

Flow decomposition for heat equations with memory

decomposition of the flow, Heat equations with memory, hybrid parabolichyperbolic phenomenon

G. Wang, Y. Zhang, E. Zuazua. Flow decomposition for heat equations with memory (2022) J. Math. Pures Appl, Vol. 158, pp 183-215, ISSN:0021-7824. https://doi.org/10.1016/j.matpur.2021.11.005 Abstract. We build up a decomposition…

Sidewise control of 1-d waves

1-d wave equations, BV-coefficients, nodal profile con-trol, sidewise controllability, sidewise energy estimates

Y. Sarac, E. Zuazua. Sidewise control of 1-d waves. J Optim Theory Appl. Vol. 193, pp. 931–949 (2022). https://doi.org/10.1007/s10957-021-01986-w Abstract. We analyze the sidewise controllability for the variable coefficients one-dimensional…

Constrained control of gene-flow models

bistable equations, Control, geneflow models, non-controllability, reaction-diffusion equations, spatial heterogeneity, staircase method

Mazari I., Ruiz-Balet D., Zuazua E. Constrained control of gene-flow models. (2021) Ann. Inst. Henri Poincare (C) Anal. Non Lineaire ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to the…

Multilevel selective harmonic modulation by duality

Biccari U, Zuazua E. Multilevel selective harmonic modulation by duality (2022) IFAC-PapersOnLine, Vol. 55, No. 16, pp. 56-61, https://doi.org/10.1016/j.ifacol.2022.08.081. Abstract. We address the Selective Harmonic Modulation (SHM) problem in power…

Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

optimal control problems, Riccati operator, slow decay rate, turnpike property, weak controllability and observability

Zhong-Jie Han, E. Zuazua, Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems (2022) SIAM J. Control Optim. Vol. 60, No. 4, pp. 2440-2468. https://dx.doi.org/10.1137/21M1441985 Abstract: This paper is devoted…

Sparse approximation in learning via neural ODEs

deep learning, Neural ODEs, Nonlinear systems, optimal control, Sparsity, Supervised Learning

Esteve C., Geshkovski B. Sparse approximation in learning via neural ODEs (2021) Abstract. We consider the continuous-time, neural ordinary differential equation (neural ODE) perspective of deep supervised learning, and study the…

Averaged dynamics and control for heat equations with random diffusion

Bárcena J.A., Zuazua E.. Averaged dynamics and control for heat equations with random diffusion (2021) Syst. Control. Lett. Vol. 158. https://doi.org/10.1016/j.sysconle.2021.105055 Abstract. This paper deals with the averaged dynamics for…

Differentiability with respect to the initial condition for Hamilton-Jacobi equations

Esteve C., Zuazua E.. Differentiability with respect to the initial condition for Hamilton-Jacobi equations (2022) SIAM Journal on Mathematical Analysis, Vol. 54, No. 5, pp. 5388-5423 https://doi.org/10.1137/22M1469353 Abstract. We prove…

Special issue in the honor of Enrique Zuazua’s 60th birthday

G. Buttazzo, E. Casas, L. de Teresa, R. Glowinski, G. Leugering, E. Trélat and X. Zhang (eds.). Special issue in the honor of Enrique Zuazua's 60th birthday (2021) ESAIM: Control, Optimisation…

Multilevel control by duality

Umberto Biccari, Enrique Zuazua. Multilevel control by duality (2023) Systems & Control Letters, Vol. 175, 105-502, https://doi.org/10.1016/j.sysconle.2023.105502 Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting in designing…

Model predictive control with random batch methods for a guiding problem

Agent-based models, Guiding problem, large scale complex systems, Random

Ko Dongnam, Zuazua Enrique. Model predictive control with random batch methods for a guiding problem (2021). Math. Models Methods Appl. Sci., Vol. 31, No. 8, pp. 1569-1592. (2021) DOI: https://doi.org/10.1142/S0218202521500329…

Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

descriptor systems, linear systems, long time behavior, optimal control, Riccati equations

Heiland J., Zuazua E. Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems (2021) SIAM J. Control Optim., Vol. 59.5 (2021), pp. 3600-3624 Abstract.…

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

Jon Asier Bárcena-Petisco. Optimal control for neural ODE in a long time horizon and applications to the classification (2021) Abstract. We study the optimal control in a long time horizon…

The turnpike property in nonlinear optimal control – A geometric approach

Nonlinear system, optimal control, Turnpike

N. Sakamoto, E. Zuazua. The turnpike property in nonlinear optimal control - A geometric approach. (2021) Automatica., Vol. 134 (2021), p. 109939 Abstract: This paper presents, using dynamical system theory,…

A quantitative analysis of Koopman operator methods for system identification and predictions

C. Zhang, E. Zuazua. A quantitative analysis of Koopman operator methods for system identification and predictions (2023) Comptes Rendus. Mécanique, Vol. 351, No. S1, pp. 1-31. In memory of R.…

Optimal control of linear non-local parabolic problems with an integral kernel

Umberto Biccari, Víctor Hernández-Santamaría, Loic Louison, Abdennebi Omrane. Optimal control of linear non-local parabolic problems with an integral kernel. (2021) Abstract. We consider a linear non-local heat equation in a bounded…

Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian type equation

Abita Rahmoune, Umberto Biccari. Blow-up results for a logarithmic pseudo-parabolic -Laplacian equation. (2021) Abstract. In this paper, we consider an initial-boundary value problem for the following mixed pseudo-parabolic p(.)-Laplacian type equation…

Local null controllability of the penalized Boussinesq system with a reduced number of controls

J.A. Bárcena-Petisco, Kevin Le Balc'H. Local null controllability of the penalized Boussinesq system with a reduced number of controls (2021) Abstract. In this paper we consider the Boussinesq system with homogeneous…

Initial data identification for the one-dimensional Burgers equation

Thibault Liard, Enrique Zuazua. Initial data identification for the one-dimensional Burgers equation. (2022). IEEE T Automat. Contr., Vol. 67, No. 6, pp. 3098-3104, DOI: 10.1109/TAC.2021.3096921 Abstract. In this paper, we…

Control of Hyperbolic and Parabolic Equations on Networks and Singular limits

advection-diffusion equations, Controllability, cost of controllability, network, singular limits, vanishing viscosity

J.A. Bárcena-Petisco, M. Cavalcante, G.M. Coclite, N. de Nitti, Enrique Zuazua. Control of Hyperbolic and Parabolic Equations on Networks and Singular limits (2021) Abstract. We study the controllability properties of the…

Controllability of one-dimensional viscous free boundary flows

B. Geshkovski, E. Zuazua. Controllability of one-dimensional viscous free boundary flows. Siam. J. Control. Optim (2021), Vol. 59, No. 3, pp. 1830–1850. https://doi.org/10.1137/19M1285354 Abstract. In this work, we address the…

The turnpike property in semilinear control

D. Pighin The turnpike property in semilinear control ESAIM Control Optim. Calc. Var., Vol. 26 (2021), pp. 1-48 Abstract.An exponential turnpike property for a semilinear control problem is proved. The…

The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms

M. Gugat, M. Schuster, E. Zuazua. The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms, in "Stabilization of Distributed Parameter Systems: Design Methods and Applications". Grigory…

Large-time asymptotics in deep learning

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

Esteve C., Geshkovski B., Pighin D., Zuazua E. Large-time asymptotics in deep learning (2021). hal-02912516 Abstract. It is by now well-known that practical deep supervised learning may roughly be cast as…

Multiplicity of solutions for fractional q(.)-Laplacian equations

Abita Rahmoune, Umberto Biccari. Multiplicity of solutions for fractional -Laplacian equations. (2021) Abstract. In this paper, we deal with the following elliptic type problem where is a measurable function and is…

Multilevel Selective Harmonic Modulation via Optimal Control

Umberto Biccari, Carlos Esteve-Yagüe, Deyviss Jesús Oroya-Villalta. Multilevel Selective Harmonic Modulation via Optimal Control. (2022) Applied Mathematics and Optimization Abstract. We consider the Selective Harmonic Modulation (SHM) problem, consisting in the…

Local null controllability of a model system for strong interaction between internal solitary waves

Jon Asier Bárcena-Petisco, Sergio Guerrero and Ademir F. Pazoto. Local null controllability of a model system for strong interaction between internal solitary waves. Commun. Contemp. Math. (2021) https://doi.org/10.1142/S0219199721500036 Abstract. In…

Control and Deep Learning: Some connections

B. Geshkovski, E. Zuazua. Control and Deep Learning: Some connections (2021) This note is an extended abstract for a talk given by the second author during the workshop ”Challenges in…

Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2022), Vol. 11, No. 1: 301-324. doi: 10.3934/eect.2021014 Abstract: We analyze the interior controllability problem for…

Nonnegative control of finite-dimensional linear systems

Dirac impulse, Minimal time, Nonnegative control

Lohéac J., Trélat E., Zuazua E. Nonnegative control of finite-dimensional linear systems. Ann. I. H. Poincare-An., Vol. 38, No. 2, pp. 301-346. (2021) DOI: https://doi.org/10.1016/j.anihpc.2020.07.004 Abstract. We consider the controllability…

Reachable subspaces, control regions and heat equations with memory

control regions, Controlled heat equations with memory, reachable subspaces

G. Wang, Y. Zhang, E. Zuazua. Reachable subspaces, control regions and heat equations with memory. (2021) Abstract. We study the controlled heat equations with analytic memory from two perspectives: reachable…

Rotor imbalance suppression by optimal control

M. Gnuffi, D. Pighin, N. Sakamoto Rotor imbalance suppression by optimal control Optimal Control Applications and Methods, Vol. 43, No. 1 (2022), pp. 213-242. Abstract. An imbalanced rotor is considered.…

Analysis and numerics solvability of backward-forward conservation laws

Backward-forward method, Conservation Laws, Identification problems, Non-smooth optimization problem, Wave-front tracking algorithm, Weak-entropy solutions

Thibault Liard, Enrique Zuazua. Analysis and numerics solvability of backward-forward conservation laws. (2020) Abstract. In this paper, we study the problem of initial data identification for the one-dimensional Burgers equation.…

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Hamilton-Jacobi equation, inverse design problem, obstacle problems, semiconcave envelopes

Esteve C., Zuazua E.. The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes SIAM J. Math. Anal., Vol. 52, No. 6, pp. 5627–5657 (2020). https://doi.org/10.1137/20M1330130 Abstract. We study the inverse…

Null-controllability of perturbed porous medium gas flow

degenerate parabolic equation, null controllability, porous medium equation, thin-ﬁlm equation

B. Geshkovski,Null-controllability of perturbed porous medium gas flow. ESAIM:COCV, vol. 26, No. 85 (2020). DOI: 10.1051/cocv/2020009 Abstract: In this work, we investigate the null-controllability of a nonlinear degenerate parabolic equation,…

Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations

Constraints, Controllability, Mathematical biology, Reaction-diffusion

Ruiz-Balet D., Zuazua E.. Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. J. Math. Pures Appl, vol. 143, pp. 345-375 (2020) https://doi.org/10.1016/j.matpur.2020.08.006 Abstract. Dynamic phenomena in social and…

Sparse source identification of linear diffusion–advection equations by adjoint methods

Adjoint problem, Diffusion–advection equation, Inverse problems, optimal control, Optimization

Monge A., Zuazua E. Sparse source identification of linear diffusion–advection equations by adjoint methods. Syst. Control. Lett, vol. 145 (2020). DOI: https://doi.org/10.1016/j.sysconle.2020.104801 Abstract: We present an algorithm for the time-inversion…