WP5-MHM

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…

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 (2021) Abstract: We analyze the interior controllability problem for a nonlocal Schr\"odinger equation involving the fractional…

Null-controllability of perturbed porous medium gas flow

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,…

Controllability of a Class of Infinite Dimensional Systems with Age Structure

admisible control operator, age structure, infinite dimensional linear system, null controllability, population dynamics

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…

Controllability of the one-dimensional fractional heat equation under positivity constraints

U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Commun. Pure Appl. Anal., Vol 19. No. 4 (2019), pp. 1949-1978. DOI: 10.3934/cppaa.2020086

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…

Null-controllability properties of a fractional wave equation with a memory term

fractional wave equation, memory term, null controllability

U. Biccari, M. Warma Null-controllability properties of a fractional wave equation with a memory term. Evol. Eq. Control The., Vol. 9, No. 2 (2020), pp. 399-430 Abstract: We study the…

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 ,…

Propagation of one and two-dimensional discrete waves under finite difference approximation

U. Biccari, A. Marica, E. Zuazua Propagation of one and two/dimensional discrete waves under finite difference approximation, Found. Comput. Math., Vol. 20 (2020), pp. 1401-1438. DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…

WKB expansion for a fractional Schrödinger equation with applications to controllability

MATLAB

Download Code related to the WKB expansion for a fractional Schrödinger equation with applications to controllability. Developed by Umberto Biccari, Alejandro B. Aceves & Enrique Zuazua

Solving an optimal control problem arised in ecology with AMPL

IpOpt/AMPL

Download Code related to the Solving an optimal control problem arised in ecology with AMPL . Developed by Jiamin ZHU & Enrique Zuazua

$plot_frac_schrodinger2_09_6$

WKB expansion for a fractional Schrödinger equation with applications to controllability

PDF version | Download Matlab Code... In [3], we develop a WKB analysis for the propagation of the solutions to the following one-dimensional nonlocal Schrödinger equation \begin{align}\label{main_eq} \mathcal{P}_s u:= \left[i\partial_t…

Finite element approximation of the 1-D fractional Poisson equation MATLAB code

MATLAB

Download Code related to the Finite element approximation of the 1-D fractional Poisson equation problem. Developed by Umberto Biccari, Victor Hernández-Santamaría & Enrique Zuazua .

Solving an optimal control problem arised in ecology with AMPL

PDF version... | Download Code... Introduction We are interested in optimal control problems subject to a class of diffusion-reaction systems that describes the growth and spread of an introduced population of…

$Finite element approximation of the 1-D fractional Poisson equation$

Finite element approximation of the 1-D fractional Poisson equation

A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control.

Control of PDEs involving non-local terms

Relevant models in Continuum Mechanics, Mathematical Physics and Biology are of non-local nature. Moreover, these models are applied for the description of several complex phenomena for which a local approach is inappropriate or limiting. In this setting, classical PDE theory fails because of non-locality. Yet many of the existing techniques can be tuned and adapted, although this is often a delicate matter...

Models involving memory terms & hybrid PDE+ODE systems (MHM)

Control theory for PDEs has been quite exhaustively developed for model problems (heat and wave equations). But other important models in applications, of hybrid nature, remain poorly understood. This is…

Controllability of one-dimensional viscous free boundary flows

Control and Deep Learning: Some connections

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

Null-controllability of perturbed porous medium gas flow

Controllability of a Class of Infinite Dimensional Systems with Age Structure

Controllability of the one-dimensional fractional heat equation under positivity constraints

A PDE-ODE model for traffic control with autonomous vehicles

Null-controllability properties of a fractional wave equation with a memory term

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

Propagation of one and two-dimensional discrete waves under finite difference approximation

WKB expansion for a fractional Schrödinger equation with applications to controllability

Solving an optimal control problem arised in ecology with AMPL

WKB expansion for a fractional Schrödinger equation with applications to controllability

Finite element approximation of the 1-D fractional Poisson equation MATLAB code

Solving an optimal control problem arised in ecology with AMPL

Finite element approximation of the 1-D fractional Poisson equation

Control of PDEs involving non-local terms

Models involving memory terms & hybrid PDE+ODE systems (MHM)

Greedy search of optimal approximate solutions

Control of reaction-diffusion models in biology and social sciences

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

Optimal actuator design via Brunovsky’s normal form

Turnpike in Optimal Control PDES, ResNets, and beyond