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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…

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…

Greedy search of optimal approximate solutions

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

Multilevel selective harmonic modulation by duality

Biccari U, Zuazua E. Multilevel selective harmonic modulation by duality (2021) Abstract. We address the Selective Harmonic Modulation (SHM) problem in power electronic engineering, consisting in designing a multilevel staircase…

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…

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 (2021) Abstract. These lecture notes address the controllability under state constraints of reaction-diffusion equations arising…

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…

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 (2021) Abstract: This paper is devoted to analysing the explicit slow decay rate and turnpike in the…

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 (2021) Abstract: In this paper, by using the Brunovsky normal form, we provide a reformulation of the problem consisting…

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…

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

Christophe Zhang, Enrique Zuazua. A quantitative analysis of Koopman operator methods for system identification and predictions (2021) Abstract. We give convergence and cost estimates for a data-driven system identification method:…

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…

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 (2021) Abstract. We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of…

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

Deyviss Jesús Oroya-Villalta, Carlos Esteve-Yagüe Umberto Biccari. Multilevel Selective Harmonic Modulation via Optimal Control. (2021) Abstract. We consider the Selective Harmonic Modulation (SHM) problem, consisting in the design of a staircase…

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…

Rotor imbalance suppression by optimal control

M. Gnuffi, D. Pighin, N. Sakamoto Rotor imbalance suppression by optimal control (2021) Abstract. An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the…

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…

Existence and cost of boundary controls for a degenerate/singular parabolic equation

Umberto Biccari, Víctor Hernández-Santamaría, Judith Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation (2020). Abstract. In this paper, we consider the following degenerate/singular parabolic equation ,…

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…

Optimal driving strategies for traffic control with autonomous vehicles

T. Liard, Raphael Stern, Maria Laura Delle Monache. Optimal driving strategies for traffic control with autonomous vehicles. (2019) Abstract. This article considers the possibility of using a small number of…

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…

Turnpike in optimal shape design for heat equation

G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design for heat equation Abstract: After a short presentation of the turnpike’s problem in optimal control, we focus on the…

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.…