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:

#### 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.

#### LQR control of a fractional reaction diffusion equation

Design of a LQR controller for the stabilization of a fractional reaction diffusion equation

#### Rays propagation of a fractional Schrodinger Equation

Solution of a fractional Schordinger equation starting from a concentrated and highly oscillatory initial datum, and display of its propagation properties along the rays of geometric optics

#### WKB expansion for a fractional Schrödinger equation with applications to controllability

Theoretical and numerical analysis of the propagation of the solutions for a Schrödinger equation with fractional Laplacian, with application to the study of controllability properties.

#### 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

#### Solving an optimal control problem arised 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