PDF version | Download Code… | 1. Problem formulation Let be an open and bounded Lipschitz Domain and consider the parameter dependent parabolic equation with Dirichlet boundary conditions (1) where is the state, is a control function and is given initial datum. In (1), is a scalar coefficient depending on some parameter and…

#### 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 , , and the discretization parameters , in the minimal computed time . Your browser does not support the video tag. Introduction In this short tutorial we explain how to use IpOpt in order 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.

#### 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…

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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**.