MTM2005-00714 – Funded by MEC – From 01/01/2006 to 31/12/2008 (January 2006-December 2008) PI: , MTM2005-00714

View More MTM2005-00714# Category: Projects

Projects (current & past) where CCM members participate/d

## MTM2008-03541 Partial Differential Equations: Analysis, Control, Numerics and Applications

(January 2009-December 2011) PI: , MTM2008-03541

View More MTM2008-03541 Partial Differential Equations: Analysis, Control, Numerics and Applications## PI2010-04

PI2010-04 – Funded by Basque Government May 2010 – December 2012 PI: FP7-295217

View More PI2010-04## High Performance Computing for Geophysics Applications

Project reference: FP7-295217 Funded by REA_PEOPLE (IRSES) Duration: January 2012 – December 2014

View More High Performance Computing for Geophysics Applications## Partial Differential Equations: Analysis, Control, Numerics and Applications

Project reference: MTM2011-29306 Project financed by the MICINN through the VI I+D+i National Plan PI: Enrique Zuazua Research Center: BCAM (C02-01) – UPM (C02-02) Duration: January 2012…

View More Partial Differential Equations: Analysis, Control, Numerics and Applications## Interplay Between Continuous-Time and Discrete-Time Optimal Control Problems

Project reference: FA9550-14-1-0214 Funded by EOARD-AFOSR – UPMC (Paris) PI: Emanuel Trélat – Université Pierre et Marie Curie, Paris Duration: July 2014 – June 2017…

View More Interplay Between Continuous-Time and Discrete-Time Optimal Control Problems## Dynamics, Control and Numerics of Fractional Partial Differential Equations

Project reference: FA9550-15-1-0027 PI: M. Warma, Univ. Puerto Rico, Río Piedras, PR Host: AFOSR – Universidad de Puerto Rico Duration: December 2014 – November 2017

View More Dynamics, Control and Numerics of Fractional Partial Differential Equations## Methods for numerical simulation and control of environmental flows platforms

Project reference: MTM2014-52347 PI: Miguel Escobedo, J. C. Peral – UPV/EHU, Bilbao Funded by MINECO Duration: October 2015 – December 2017

View More Methods for numerical simulation and control of environmental flows platforms## Groupement Euro-Maghrébin de Mathématiques et de leurs Interactions

Web page of the project.

View More Groupement Euro-Maghrébin de Mathématiques et de leurs Interactions## ICON – Interactions of Control, Partial Differential Equations and Numerics

This project aims at making a breakthrough contribution in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by…

View More ICON – Interactions of Control, Partial Differential Equations and Numerics## Control y problemas inversos – COPI

December 2015-December 2017 PI: E. Fdez. Cara, Universidad de Sevilla MTM2015-70444-REDT Web page of the event

View More Control y problemas inversos – COPI## IpOpt and AMPL use to solve time optimal control problems

PDF version… | Download Code… Featured Video Evolution of the controls and of the state for $y^0=1$, $y^1=5$, $M=20$ and the discretization parameters $N_x=30$, $N_t=450$ in…

View More IpOpt and AMPL use to solve time optimal control problems## 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.

View More Finite element approximation of the 1-D fractional Poisson equation## Turnpike property for functionals involving L^{1}−norm

We want to study the following optimal control problem:

\begin{equation*}

\left(\mathcal{P}\right) \ \ \ \ \ \ \ \hat{u}\in\argmin_{u\in L^2_T} \left\{J\left(u\right)=\alpha_c \norm{u}_{1,T} + \frac{\beta}{2}\norm{u}^2_{T}+\alpha_s \norm{Lu}_{1,T} + \frac{\gamma}{2}\norm{Lu-z}_{T}^2\right\},

\end{equation*}

^{1}−norm

## 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…

View More Conservation laws in the presence of shocks## 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…

View More Numerical aspects of LTHC of Burgers equation## 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…

View More Long time control and the Turnpike property## 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…

View More Control of PDEs involving non-local terms## 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**.

## Optimal control applied to collective behaviour

The standard approach for solving a driving problem is a leadership strategy, based on the attraction that a driver agent exerts on other agent. Repulsion forces are mostly used for collision avoidance, defending a target or describing the need for personal space. We present a “guidance by repulsion” model describing the behaviour of two agents, a driver and an evader…

View More Optimal control applied to collective behaviour## Greedy Control

Control of a parameter dependent system in a robust manner. Fix a control time $T > 0$, an arbitrary initial data $x^0$, and a final target $x^1 \in R^N$…

View More Greedy Control## From finite to infinite-dimensional models (FI)

Our team has made several contributions in the description of the limit behaviour, as the mesh sizes tend to zero, of numerical schemes for wave…

View More From finite to infinite-dimensional models (FI)## Models involving memory terms & hybrid PDE+ODE systems (MHM)

Control theory for PDEs has been quite exhaustively developed for model problems (heat and wave equations). But other important models in applications, of hybrid nature,…

View More Models involving memory terms & hybrid PDE+ODE systems (MHM)## Inverse design and control in the presence of singularities (SINV)

Some important PDE models in Continuum Physics, such as hyperbolic conservation laws, represent a major challenge from a control viewpoint for two (closely related) reasons:…

View More Inverse design and control in the presence of singularities (SINV)## Control under constraints (CC)

Most of the existing theory of controllability for PDEs has been developed in the absence of constraints on the controls and states. Thus, in practice,…

View More Control under constraints (CC)## Long time horizon control (LTHC)

Control problems for evolution PDEs are most often considered in finite time intervals, without paying attention to the length of the control horizon and how…

View More Long time horizon control (LTHC)## Control of parameter dependent problems (PDC)

In real applications, models are not completely known since relevant parameters (deterministic or stochastic) are subject to uncertainty and indetermination. Accordingly, for practical purposes, robust…

View More Control of parameter dependent problems (PDC)## Projects

The Chair of Computational Mathematics is meant to hold projects related to various aspects of Applied Mathematics including **Partial Differential Equations (PDE), Numerical Analysis, Control theory and Optimal Design**. These interconnected fields have as goal the modelling, analysis, computer simulation and control and design of natural phenomena and engineering processes arising in several contexts of research, development and innovation (R+D+i)…