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.
Numerical computation of a stabilizing control
Stabilization of a coupled PDE-ODE system by means of a feedback LQR control.
Design of a LQR controller for the stabilization of a fractional reaction diffusion 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
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.
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