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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 (2022) Abstract. This paper is concerned with a combination of Random Batch Methods (RBMs) and…

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) Abstract. We give a full characterization of the range of the operator which…

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…

Gaussian Beam ansatz for finite difference wave equations

Biccari U, Zuazua E. Gaussian Beam ansatz for finite difference wave equations (2022) Abstract. This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation…

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…

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…

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…

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…

Analysis and numerical solvability of backward-forward conservation laws

Thibault Liard, Enrique Zuazua. Analysis and numerical solvability of backward-forward conservation laws (2022) Abstract. In this paper, we study the problem of initial data identification for weak-entropy solutions of the…

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 (2022) Abstract. We consider the problem of identifying…

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…

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 (2021) Abstract. We prove that the viscosity solution to a Hamilton-Jacobi equation with a smooth convex…

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 (2021) Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in…

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…

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…

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…

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…

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…

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…

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 turnpike with lack of observability

Pighin D., Sakamoto N. The turnpike with lack of observability (2020) Abstract: We obtain turnpike results for optimal control problems with lack of stabilizability in the state equation and/or detectability 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…

Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term

heat equation, singular limits, spectral decomposition, transport equation, uniform controllability

Bárcena-Petisco J.A., Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term (2020). HAL Id: hal-02455632 Abstract. In this paper we consider the heat equation with…

A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diﬀusive models

I. Mazari, D. Ruiz-Balet. A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diﬀusive models (2020) Abstract. Following the recent works [9, 17,…

Asymptotic behavior of scalar convection-diffusion equations

Enrique Zuazua. Asymptotic behavior of scalar convection-diffusion equations (2020) Abstract. In these lecture notes, we address the problem of large-time asymptotic behaviour of the solutions to scalar convection-diffusion equations set in…

A PDE-ODE model for traffic control with autonomous vehicles

Thibault Liard, Raphael Stern, Maria Laura Delle Monache. A PDE-ODE model for traffic control with autonomous vehicles. (2020) Abstract. We introduce a coupled PDE-ODEs model to describe mixed traffic with…

A controlled multiscale model for traffic regulation via autonomous vehicles

T. Liard, . A controlled multiscale model for traffic regulation via autonomous vehicles. (2019) Abstract. Autonomous vehicles ($AV$s) allow new ways of regulating the traffic flow on road networks. Most…

On entropic solutions to conservation laws coupled with moving bottlenecks

T. Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. (2019) Abstract. Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled…

Inverse design for the one-dimensional Burgers equation

T. Liard, E. Zuazua. Inverse design for the one-dimensional Burgers equation. (2019) Abstract. In this paper, we study the problem of inverse design for the one-dimensional Burgers equation. This problem…

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

Antil H, Biccari U, Ponce R, Warma M, Zamorano S. Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation Abstract. We study the controllability to…

Model reduction of converter-dominated power systems by Singular Perturbation Theory

U. Biccari, N. Sakamoto, E. Unamuno, D. Madariaga, E. Zuazua, J.A. Barrena. Model reduction of converter-dominated power systems by Singular Perturbation Theory Abstract: The increasing integration of power electronic devices is driving the development of more advanced tools and methods for…

Mathematical model to asses impact of vih/aids infection in the spread of tuberculosis

Nkamba L. Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis (2019) Abstract: Tuberculosis is a serious problem of public health in several countries.…