Our recent contributions in this area are inspired in the interpretation of memory models as the **coupling of PDEs with infinite-dimensional ODEs**. The presence of ODE components in the system explains the failure of controllability if the control is confined on a space-support which is time-independent. This motivates the use of our **moving control strategy**, making the control move covering the whole domain, introducing the transport effects that the ODE is lacking.

#### Available tutorials:

#### Moving control strategy for memory-type equations

Numerical implementation of the moving control strategy for a two dimensional heat equation with memory

#### Simulation of Fractional Heat Equation

In this tutorial, we show the simulation of heat fractional equation

#### Optimal Control of the Fokker-Planck Equation with CasADi

In this tutorial, we present an optimal control problem related to the Fokker-Planck equation.

#### Numerical simulation of nonlinear Population Dynamics Structuring by age and Spatial diffusion

In this tutorial, we propose the Hum method to approximate numerically the control in a null controllability problem for a non linear population dynamics model structuring in age and spatial diffusion.

#### Controllability of a Class of Infinite Dimensional Systems with Age Structure

In this tutorial, we investigate the linear infinite dimensional system obtained by implementing an age structure to a given linear dynamical system. We show that if the initial system is null controllable in a time small enough, then the age structured system is also null controllable in a time depending on the various involved parameters.

#### Finite Element approximation of the one-dimensional fractional Laplacian

We describe a FE method for the approximation of the one-dimensional fractional Laplacian $(-d_x^2)^s$ on a uniform mesh discretizing the symmetric interval $(-L,L)$, $L>0$.

#### A numerical method for solving an age structured virus model

We consider an age-structured HIV infection model with a general nonlinear infection function. The numerical method to solve this system of equation is based on the upwind method for solving hyperbolic partial differential equation and the ODEs are solving by explicit Euler method.

#### A reaction-diffusion equation with delay

The aim of this tutorial is to give a numerical method for solving a partial differential equation with a constant delay.

#### The Dirichlet-Neumann iteration for two coupled heterogeneous heat equations

This tutorial explains how to use the Dirichlet-Neumann method to coordinate the numerical solutions of two linear heat equations with strong jumps in the material coefficients accross a common interface.

#### LQR controller for stabilizing the linear population dynamics model

In this tutorial, we will demonstrate how to design a LQR controller in order to stabilize the linear population dynamics model dependent on age and space

#### Coupled transport equations and LQR control

Numerical computation of a stabilizing control

#### LQR optimal control design for a coupled PDE-ODE system.

Stabilization of a coupled PDE-ODE system by means of a feedback LQR control.

#### Solving an optimal control problem arisen in ecology with AMPL

We present a computational tool to solve optimal control problems for diffusion-reaction systems describing the growth and spread of populations