Sharp numerical approximation of the Hardy constant
L. Ignat, E. Zuazua (2025) Sharp numerical approximation of the Hardy constant Abstract. We study the P1 finite element approximation of the best constant in the classical Hardy inequality over…
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, SIAM Mathematics of Data Science, SIMODS, arxiv: 2407.01602 Abstract. Transformers are…
A potential game perspective in Federated Learning
K. Liu, Z. Wang, E. Zuazua (2025) A potential game perspective in Federated Learning, arxiv:2411.11793 Abstract. Federated learning (FL) is an emerging paradigm for training machine learning models across distributed…
Regional and Partial Observability and Control of Waves
B. Dehman, S. Ervedoza, E. Zuazua (2025) Regional and Partial Observability and Control of Waves Abstract.We establish sharp regional observability results for solutions of the wave equation in a bounded…
Cluster-based classification with neural ODEs via control
A. Alvarez-Lopez, R. Orive-Illera, E. Zuazua (2025) Optimized classification with neural odes via separability, J. Mach. Learn., arXiv:2312.13807v2 Abstract.We address binary classification using neural ordinary differential equations from the perspective…
Optimal convergence rates for the finite element approximation of the Sobolev constant
L. Ignat, E. Zuazua (2025) Optimal convergence rates for the finite element approximation of the Sobolev constant Abstract. We establish optimal convergence rates for the P1 finite element approximation of…
Boundary observation and control for fractional heat and wave equations
U. Biccari, E. Zuazua (2025) Boundary observation and control for fractional heat and wave equations, https://doi.org/10.48550/arXiv.2504.17413 Abstract. We establish boundary observability and control for the fractional heat equation over arbitrary…
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, arXiv: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., Vol. 35, No. 6, pp. 1471-1521, arXiv:2412.01619v1, https://doi.org/10.1142/S0218202525500228 Abstract. In…
Exact Sequence Classification with Hardmax Transformers
A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025) Exact Sequence Classification with Hardmax Transformers, arxiv: 2502.02270 Abstract. We prove that hardmax attention transformers perfectly classify datasets of $N$ labeled sequences…
On the decay of one-dimensional locally and partially dissipated and hyperbolic systems
T. Crin-Barat, N. De Nitti, E. Zuazua (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
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…
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…
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, arXiv: 2407.17092 Abstract. In this paper, we introduce semi-autonomous neural ordinary…
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…
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. Hernandez, E. Zuazua (2025)Deep Neural Networks: Multi-Classification and Universal Approximation arXiv:2409.06555 Abstract. We demonstrate that a ReLU deep neural network with a width of 2 and a depth of…
Approximate and Weighted Data Reconstruction Attack in Federated Learning
Z. Wang, 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 clients…
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…
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.W.M. 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, E. Zuazua. 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…
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 (2025)Tracking controllability for finite-dimensional linear systems arXiv:2407.18641v2 Abstract. In this work, we present a functional analytic framework for tracking controllability in finite-dimensional linear systems. By leveraging…
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…
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 (2025) Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings, Mathematical Models and Methods…
Optimal Placement and Shape Design of Sensors via Geometric Criteria
I. Ftouhi, E. Zuazua (2024) Optimal Placement and Shape Design of Sensors via Geometric Criteria, 2024 European Control Conference (ECC), Stockholm, Sweden, 2024, pp. 834-837, doi: 10.23919/ECC64448.2024.10591236 Abstract. The optimal…
Control of a Lotka-Volterra System with Weak Competition
M. Sonego, E. Zuazua (2024)Control of a Lotka-Volterra System with Weak Competition, arXiv:2409.20279 Abstract. The Lotka-Volterra model reflects real ecological interactions where species com- pete for limited resources, potentially leading…
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 Abstract. Neural ordinary…
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
R. 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
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…
Special Issue Dedicated to the Memory of Professor Roland Glowinski
A. Quaini, X. Qin, X. Tai, E. Zuazua (2025)Special Issue Dedicated to the Memory of Professor Roland Glowinski, AMSA, Vol. 8, No. 3, pp. 407 – 409 8 articles in:…
Control of reaction-diffusion models in biology and social sciences
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…
Sidewise Control
E. Zuazua (2023) Sidewise Control "Control methods in Hyperbolic PDEs", Oberwolfach, November 2023, DOI:10.4171/OWR/2023/52, pp. 62-63 "Inspired on [1] and [4], we explored the lateral or sidewise control properties of…
Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws
C. Esteve, E. Zuazua. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws Nonlinear Analysis, Vol. 227, https://doi.org/10.1016/j.na.2022.113167 Abstract. We give a full characterization of the range…
Constrained control of gene-flow models
I. Mazari, D. Ruiz-Balet, E. Zuazua (2023)Constrained control of gene-flow models, Ann. Inst. Henri Poincare (C) Anal. Non Lineaire ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to the transfer…
Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave
G.M. Coclite, N. De Nitti, E. Zuazua (2023) Long-time convergence of a nonlocal Burgers' equation towards the local N-wave, CVGMT Nonlinearity, Vol. 36, No. 11, pp. 5998-6019, DOI: 10.1088/1361-6544/acf01d Abstract.…
Greedy search of optimal approximate solutions
M. Lazar, E. Zuazua (2023) Greedy search of optimal approximate solutions Pure and Applied functional Analysis, Vol. 8, No. 2, pp. 547-564, http://yokohamapublishers.jp/online2/oppafa/vol8/p547.html Abstract. In this paper we develop a…
Multilevel control by duality
U. Biccari, E. Zuazua (2023) Multilevel control by duality 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…
Neural ODE Control for Classification, Approximation and Transport
D. Ruiz-Balet, E. Zuazua (2023)Neural ODE Control for Classification, Approximation and Transport, SIAM Review, Vol. 65, No. 3, pp. 735-773, https://doi.org/10.1137/21M1411433 Abstract. We analyze Neural Ordinary Differential Equations (NODEs) from…
A quantitative analysis of Koopman operator methods for system identification and predictions
C. Zhang, E. Zuazua (2023) A quantitative analysis of Koopman operator methods for system identification and predictions, Comptes Rendus. Mécanique, Vol. 351, No. S1, pp. 1-31. In memory of R.…
Optimal design of sensors via geometric criteria
I. Ftouhi, E. Zuazua (2023) Optimal design of sensors via geometric criteria, 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…
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…
Analysis and numerical solvability of backward-forward conservation laws
T. Liard, E. Zuazua (2023) Analysis and numerical solvability of backward-forward conservation laws SIAM Journal on Mathematical Analysis, Vol. 55, No. 3, pp. 1949-1968, https://doi.org/10.1137/22M1478720 Abstract. In this paper, we…
On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov methods
N. Nitti, E. Zuazua (2023) On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov methods, Vietnam J. Math. https://doi.org/10.1007/s10013-022-00598-9 Abstract. In this note, we…
Multilevel selective harmonic modulation by duality
U. Biccari, E. Zuazua 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…
Optimal actuator design via Brunovsky’s normal form
B. Geshkovski, E. Zuazua (2022) Optimal actuator design via Brunovsky's normal form, IEEE Automatic Control, Vol. 26, No. 12, DOI: 10.1109/TAC.2022.3181222 Abstract: In this paper, by using the Brunovsky normal…
Differentiability with respect to the initial condition for Hamilton-Jacobi equations
C. Esteve, E. Zuazua. 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…
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…
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…
Turnpike in Optimal Control PDES, ResNets, and beyond
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
D.W.M. Veldman, E. Zuazua (2022) A framework for randomized time-splitting in linear-quadratic optimal control Numerische Mathematik, Vol. 151, No. 2, DOI: 10.1007/s00211-022-01290-3 Abstract. Inspired by the successes of stochastic algorithms in…
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…
Control and Numerical approximation of Fractional Diffusion Equations
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
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
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…
Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems
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…
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…
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…
Model predictive control with random batch methods for a guiding problem
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
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.…
The turnpike property in nonlinear optimal control – A geometric approach
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,…
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…
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 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…
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…
Nonnegative control of finite-dimensional linear systems
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
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…
Analysis and numerics solvability of backward-forward conservation laws
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
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…
Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
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
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…
Controllability of a Class of Infinite Dimensional Systems with Age Structure
Maity D., Tucsnak M., Zuazua E. Controllability of a Class of Infinite Dimensional Systems with Age Structure. Control Cybern. Vol. 48 (2020), No. 2, pp. 231-260 hal-01964612v2 Abstract: Given a…
Shape turnpike for linear parabolic PDE models
Lance G., Trélat E., Zuazua E. Shape turnpike for linear parabolic PDE models Syst. Control. Lett. Vol. 142 (2020). DOI: 10.1016/j.sysconle.2020.104733 Abstract: We introduce and study the turnpike property for…
A stochastic approach to the synchronization of coupled oscillators
Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front. Energy Res. Vol. 8 (2020). DOI: 10.3389/fenrg.2020.00115 Abstract. This paper…
Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions
J.-C. Cortes, A. Navarro-Quiles, J.-V. Romero, M.-D. Rosello, E. Zuazua. Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions. J. Franklin I. (2020)…
Turnpike in optimal shape design
G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design IFAC-PapersOnline, Vol. 52, No. 16 (2019), pp. 496-501, ISSN: 24058963, DOI: 10.1137/17M1119160 Abstract: We investigate the turnpike problem in…
Stochastic optimization methods for the simultaneous control of parameter-dependent systems
Umberto Biccari, Ana Navarro-Quiles, Enrique Zuazua. Stochastic optimization methods for the simultaneous control of parameter-dependent systems (2020) Abstract. We address the application of stochastic optimization methods for the simultaneous control of…
Asymptotic behavior and control of a “guidance by repulsion” model
Dongnam Ko, E. Zuazua, Asymptotic behavior and control of a "guidance by repulsion" model. Math Models Methods Appl. Sci. Vol. 30, No. 04, pp. 765-804 (2020).DOI:10.1142/S0218202520400047 Abstract. We model and…