## MTM2005-00714

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

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## PI2010-04

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

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## Turnpike property for functionals involving L1−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*}

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## 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…

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## 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…

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## 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…

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## 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…

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## 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…

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## 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 $x^1 \in R^N$…

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## 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,…

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## 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…

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## 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…

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## 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)…

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