** | Download Code** related to Finite element approximation of the 1-D fractional Poisson equation.

**Developed by Umberto Biccari, Víctor Hernández-Santamaría & Enrique Zuazua**

#### 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.

#### Turnpike property for functionals involving L^{1}−norm

We want to study the following optimal control problem:

#### Conservation laws in the presence of shocks

PDF version… The problem We analyze a model tracking problem for a 1D scalar conservation law. It consists in optimizing the initial datum so to minimize a weighted distance to a given target during a given finite time horizon. To be more precise, given a finite time , a target function , and a positive…

#### Numerical aspects of LTHC of Burgers equation

This issue is motivated by the challenging problem of sonic-boom minimization for supersonic aircrafts, which is governed by a Burgers-like equation. The travel time of the signal to the ground is larger than the time scale of the initial disturbance by orders of magnitude and this motivates our study of large time control of the sonic-boom propagation…

#### Long time control and the Turnpike property

The turnpike property establishes that, when a general optimal control problem is settled in large time, for most of the time the optimal control and trajectories remain exponentially close to the optimal control and state of the corresponding steady-state or static optimal control problem…

#### Control of PDEs involving non-local terms

Relevant models in Continuum Mechanics, Mathematical Physics and Biology are of non-local nature. Moreover, these models are applied for the description of several complex phenomena for which a local approach is inappropriate or limiting. In this setting, classical PDE theory fails because of non-locality. Yet many of the existing techniques can be tuned and adapted, although this is often a delicate matter…

#### IpOpt/AMPL code sample

** | Download Code** related to the IpOpt and AMPL use to solve time optimal control problems.

**Developed by Jérôme Lohéac, Emmanuel Trélat & Enrique Zuazua**

#### Greedy Control MATLAB code

** | Download Code** related to the Greedy Control problem.

**Developed by Martin Lazar & Enrique Zuazua**.

#### Work Packages

DyCon project identifies and focuses on six key topics that play a central role in most of the processes arising in applications, but which are still poorly understood, namely: control of parameter dependent problems, long time horizon control…