One of the main outputs of the research conducted within DyCon is the development of new computational methods and tools (algorithms, tutorials, sample codes, software and simulations), all of which are being integrated in a computational platform. This page offers a higher layer of the work that is currently taking place inside the DyCon team.

All of the content has been classified according to the project’s corresponding working packages:

WP1: Control of parameter dependent problems (PDC)

Averaged Control
Numerical study of the averaged control with the steepest descent and conjugate gradient methods

A Matlab guide for the numerical approximation of the exact control and stabilization of the wave equation

Greedy algorithm for Parametric Vlasov-Fokker-Planck System
Short report about the greedy algorithm of linear Vlasov-Fokker-Planck equation, including 6 numerical experiments with figures, and corresponding matlab coding and the explanation of how to implement it.

Greedy optimal control for elliptic problems and its application to turnpike problems
Turnpike theory and greedy algorithms, applied to the steady-state elliptic control problem, are combined to obtain a greedy approximation of parabolic optimal control problems, independent of the initial data

Evolution of the solution to the semi-discretised problem for heat eq. Greedy Control
Control of a parameter dependent system in a robust manner

WP2: Long time horizon control and the turnpike property (LTHC)

Turnpike property for functionals involving L1−norm
We want to study the following optimal control problem...

Numerical aspects of LTHC of Burgers equation
Numerical approximation of the inverse design problem for the Burgers equation

The turnpike property illustrated Long time control and the Turnpike property
The turnpike property improves the numerical methods used to solve optimal control problems

WP3: Control under constraints (CC)

Control of the semi-discrete 1D heat equation under nonnegative control constraint
Using IpOpt to get the time-optimal nonnegative control of a semi-discrete 1D heat equation

IpOpt and AMPL use to solve time optimal control problems
How to use IpOpt to solve time optimal control problems

WP4: Inverse design and control in the presence of singularities (SINV)

2D inverse design of linear transport equations on unstructured grids
Various discrete adjoint methodologies are discussed for the inverse design of linear transport equations in 2 space dimensions

Conservation laws in the presence of shocks
Tracking control of 1D scalar conservation laws in the presence of shocks

WP5: Models involving memory terms and hybrid PDE+ODE systems (MHM)

plot_frac_schrodinger2_09_6 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.

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

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

Cars and Viscoelasticity Control of PDEs involving non-local terms
The problem of controllability of fractional (in time) Partial Differential Equations

WP6: From finite to infinite-dimensional models (FI)

Kolmogorov equation
Various numerical approximation methods are discussed with the aim of recoving the large time asymptotic properties of the hypoelliptic Kolmogorov model

Circunvection force. Optimal control applied to collective behaviour
"Guidance by repulsion” model describing the behaviour of two agents, a driver and an evader

Other topics

Figure 2.b Optimal Control of the Poisson Equation with OpenFOAM
How to use OpenFOAM to solve optimal control problems