Publications – cmc.deusto.eus

Turnpike in optimal control and beyond: a survey

E. Trélat, E. Zuazua (2025)Turnpike in optimal control and beyond: a survey https://hal.science/hal-05002039 Abstract. The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide…

Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach

T. Crin-Barat, L. Liverani, Ly Shou, E. Zuazua (2025)Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach https://arxiv.org/abs/2503.00236 Abstract. We study the stability of one-dimensional linear hyperbolic systems…

Pointwise constraints for scalar conservation laws with positive wave velocity

N. De Nitti, D. Serre, E. Zuazua (2025) Pointwise constraints for scalar conservation laws with positive wave velocity Abstract. We consider a conservation law with strictly positive wave velocity and…

Gaussian Beam ansatz for finite difference wave equations

U. Biccari, E. Zuazua (2025) Gaussian Beam ansatz for finite difference wave equations, Found Comput Math. , Vol. 25, pp. 1–54, https://doi.org/10.1007/s10208-023-09632-9 Abstract. This work is concerned with the construction…

Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics

K. Liu, E. Zuazua (2025) Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics Math. Models Methods Appl. Sci., arXiv:2412.01619v1 Abstract. In this work, we address three non-convex…

Exact Sequence Classification with Hardmax Transformers

A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025)Exact Sequence Classification with Hardmax Transformers Abstract. We prove that hardmax attention transformers perfectly classify datasets of $N$ labeled sequences in , .…

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

Crin-Barat T., De Nitti N., Zuazua E. (2025) On the decay of one-dimensional locally and partially dissipated and hyperbolic systems, ESAIM:COCV, https://arxiv.org/abs/2206.00555 Abstract. We study the time-asymptotic behavior of linear…

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, E. Zuazua (2025) Control of Hyperbolic and Parabolic Equations on Networks and Singular limits, MCRF, Vol. 15, No. 1, March 2025,…

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

Y. Song, Z. Wang, E. Zuazua (2025)FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning, Neural Networks, pp. 106-772, ISSN 0893-6080, https://doi.org/10.1016/j.neunet.2024.106772 Abstract. Federated learning (FL) is a promising framework…

Optimal L^p-approximation of convex sets by convex subsets

F. Zakaria, I. Ftouhi, E. Zuazua (2025)Optimal L^p-approximation of convex sets by convex subsets Abstract. Given a convex set Ω of R n, we consider the shape optimization problem of…

Tracking controllability for the heat equation

J.A. Barcena-Petisco, E. Zuazua (2025) Tracking controllability for the heat equation, IEEE Trans. Autom. Control Abstract. We study the tracking or sidewise control- lability of the heat equation. More precisely,…

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

Z. Li, K. Liu, L. Liverani, E. Zuazua (2025)Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications Abstract. In this paper, we introduce semi-autonomous neural ordinary differential equations…

Boundary sidewise observability of the wave equation

B. Dehman, E. Zuazua (2025) Boundary sidewise observability of the wave equation J. Eur. Math. Soc. (JEMS) Abstract. The wave equation on a bounded domain of Rn with non homogeneous…

Pattern control via diffusion interaction

D. Ruiz-Balet, E. Zuazua (2025)Pattern control via diffusion interaction Abstract. We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection…

Local Stability and Convergence of Unconstrained Model Predictive Control

D. Veldman, E. Zuazua (2025) Local Stability and Convergence of Unconstrained Model Predictive Control Abstract. The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based…

Deep Neural Networks: Multi-Classification and Universal Approximation

M. Hernández, E. Zuazua (2025)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…

Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis

A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025)Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis Abstract. Transformers are extremely successful machine learning models whose mathematical properties remain…

Almost periodic turnpike phenomenon for time-dependent systems

S. Zamorano (2025)Almost periodic turnpike phenomenon for time-dependent systems Systems and Control Letters Abstract. This paper explores the turnpike behavior of a controlled system with almost periodic inputs and a…

A note on the eigenvalues of a Sylvester-Kac matrix with off-diagonal biperiodic perturbations

Z. Du, C.M. da Fonseca (2025) A note on the eigenvalues of a Sylvester-Kac matrix with off-diagonal biperiodic perturbations, Journal of Computational and Applied Mathematics 461 (2025) 116429, 10.1016/j.cam.2024.116429 Abstract.…

Computational performance of the MMOC in the inverse design of the Doswell frontogenesis equation

A. Francisco, U. Biccari, E. Zuazua (2025)Computational performance of the MMOC in the inverse design of the Doswell frontogenesis equation Abstract. Inverse design of transport equations can be addressed by…

Observability for heat equations with time-dependent analytic memory

G. Wang, Y. Zhang, E. Zuazua (2024) Observability for heat equations with time-dependent analytic memory Arch Rational Mech Anal, Vol. 248, No. 115, https://doi.org/10.1007/s00205-024-02058-9 Abstract. This paper presents a complete…

Progress and future directions in machine learning through control theory

E. Zuazua (2024)Progress and future directions in machine learning through control theory Proceedings book FGS 2024, pp. 116, https://hdl.handle.net/10651/74677 Abstract. This paper presents our recent advancements at the intersection of…

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…

Stability and Convergence of a Randomized Model Predictive Control Strategy

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

Exact Controllability and Stabilization of the Wave Equation

E. Zuazua. Exact Controllability and Stabilization of the Wave Equation (2024) UNITEXT (La Matematica per il 3+2, UNITEXTMAT) - Springer Cham, Vol. 162, No. 1, eBook ISBN 978-3-031-58857-0, https://link.springer.com/book/10.1007/978-3-031-58857-0, arxiv:2402.17894…

Control and Machine Learning

E. Zuazua (2024) Control and Machine Learning Proceedings of the 9th. International Conference on Control and Optimization with Industrial Applications, August 27-29, 2024, Istanbul, Turkey Abstract. In this talk, we…

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…

Finite element approximation of the Hardy constant

F. Della Pietra, G. Fantuzzi, LI Ignat, AL Masiello, G. Paoli, E. Zuazua (2024)Finite element approximation of the Hardy constant J. Convex Anal. Special Issue Giuseppe Buttazzo 70 Abstract. We…

Approximate and Weighted Data Reconstruction Attack in Federated Learning

E. Wang E, Y. Song, E. Zuazua (2025) Approximate and Weighted Data Reconstruction Attack in Federated Learning arXiv:2308.06822 Abstract. Federated Learning (FL) is a distributed learning paradigm that enables multiple…

Control of neural transport for normalising flows

D. Ruiz-Balet, E. Zuazua (2024)Control of neural transport for normalising flows J. Math. Pures Appl., Vol. 181, pp. 58-90, ISSN 0021-7824. https://doi.org/10.1016/j.matpur.2023.10.005 Abstract. Inspired by normalizing flows, we analyze the…

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…

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…

The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries,

C.M. da Fonseca, C. Kızılateş, N. (2024) The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries, Logic Journal of the IGPL, jzae065, 10.1093/jigpal/jzae065…

Revisiting some r-Fibonacci sequences and Hessenberg matrices

C.M. da Fonseca, P. Saraiva, A.G. Shannon (2024) Revisiting some -Fibonacci sequences and Hessenberg matrices, Notes on Number Theory and Discrete Mathematics, Vol. 30, pp. 704-715, 10.7546/nntdm.2024.30.4.704-715 Abstract. The relationship…

A new generalization of min and max matrices and their reciprocals counterparts

C.M. da Fonseca, C. Kızılateş, N. (2024) A new generalization of min and max matrices and their reciprocals counterparts, Filomat, Vol. 38, pp. 421-435, 10.2298/FIL2402421F Abstract. In this paper, we…

Equitable partitions and spectra of symmetric trees: Revisiting Heilbronner’s composition principle

M. Anđelić, C.M. da Fonseca (2024) Equitable partitions and spectra of symmetric trees: Revisiting Heilbronner's composition principle, Discrete Mathematics Letters, Vol. 14, pp. 108-117, 10.47443/dml.2024.160 Abstract. The notion of equitable…

On Chebyshev polynomials and the inertia of certain matrices

K. Castillo, C.M. da Fonseca, J. Petronilho (2024) On Chebyshev polynomials and the inertia of certain matrices, Applied Mathematics and Computation, Vol. 467, pp. 128-497, 10.1016/j.amc.2023.128497 Abstract. It was first…

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…

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…

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 (2024) Interplay between depth and width for interpolation in neural ODEs, Neural Networks, Vol. 180, pp. 106-640, https://doi.org/10.1016/j.neunet.2024.106640, ISSN 0893-6080, arXiv.2401.09902 Abstract. Neural…

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 (2024) Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings 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 (2024) Uniform Turnpike Property and Singular Limits Acta Appl. Math., Vol. 190, No. 3, https://doi.org/10.1007/s10440-024-00640-7 Abstract. Motivados por límites singulares para problemas de control óptimo a…

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,…

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…

Large-time asymptotics in deep learning

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

C. Esteve, B. Geshkovski, D. Pighin, E. Zuazua (2025) Large-time asymptotics in deep learning, https://hal.archives-ouvertes.fr/hal-02912516 Abstract. We consider the neural ODE perspective of supervised learning and study the impact of the…

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

D. Ruiz-Balet, E. Zuazua (2024) Control of reaction-diffusion models in biology and social sciences Math. Control Relat. Fields, Vol. 12, No. 4, pp. 955-1038, https://doi.org/10.3934/mcrf.2022032 Abstract. These lecture notes address…

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.…

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

U. Biccari, Y. Song, X. Yuan, E. Zuazua (2023) A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation Inverse Problems, Vol. 39, No. 9, IP-103963,…

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…

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…

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…

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,…

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…

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…

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.…

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…