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.
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.
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 $(-L,L)$, $L>0$.
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.
The aim of this tutorial is to give a numerical method for solving a partial differential equation with a constant delay.
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.
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
Numerical computation of a stabilizing control
Stabilization of a coupled PDE-ODE system by means of a feedback LQR control.
A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control
We present a computational tool to solve optimal control problems for diffusion-reaction systems describing the growth and spread of populations