## WKB expansion for a fractional Schrödinger equation with applications to controllability

PDF version | Download Matlab Code... In [3], we develop a WKB analysis for the propagation of the solutions to the following one-dimensional nonlocal Schrödinger equation \begin{align}\label{main_eq} \mathcal{P}_s u:= \left[i\partial_t…

## Optimal Control of the Poisson Equation with OpenFOAM

PDF version | Download Openfoam Code... | In this tutorial, we show how to use the C++ library OpenFOAM (Open Field Operation and Manipulation) in order to solve control problems…

## Control of the semi-discrete 1D heat equation under nonnegative control constraint

PDF version...  |   Download Code... 1 Introduction In the post IpOpt and AMPL use to solve time optimal control problems, we explain how to use IpOpt and AMPL in order to…

## Wavecontrol

Manual PDF   |   Download Code... A Matlab guide for the numerical approximation of the exact control and stabilization of the wave equation This webpage contains a free software to compute…

## Greedy algorithm for Parametric Vlasov-Fokker-Planck System

PDF version...  |   Download Code... 1. Numerical experiments Consider the one dimensional linear Vlasov-Fokker-Planck (VPFP) as following. \begin{cases} \delta\pt_tf + \sigma_1v\delta\pt_x f - \frac{\sigma_2}{\epsilon} \delta\pt_x\phi\delta\pt_v f =\frac{\sigma_3}{\epsilon}\delta\pt_v\ (v f +\delta\pt_vf\…

## Solving an optimal control problem arised in ecology with AMPL

PDF version...  |   Download Code... Introduction We are interested in optimal control problems subject to a class of diffusion-reaction systems that describes the growth and spread of an introduced population of…

## Kolmogorov equation

Read PDF version  |   Download Code 1 Introduction We are interested in the numerical discretization of the Kolmogorov equation [12] where $\mu>0$ is a diffusive function and $v$ a potential function.…

## 2D inverse design of linear transport equations on unstructured grids

PDF version...   1. Adjoint estimation: low or high order? Adjoint methods have been systematically associated to the optimal control design [5] and their applications to aerodynamics [1, 4]. During the…

## Greedy optimal control for elliptic problems and its application to turnpike problems

PDF version  |   Download Code... 1. Problem formulation Let $\Omega\subset \mathbb R^d$ be an open and bounded Lipschitz Domain and consider the parameter dependent parabolic equation with Dirichlet boundary conditions where…

## 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 the minimal computed time $T\simeq\mathtt{0.2093}$.…

## 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 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*}

## 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…

## 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...

## 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...

## 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 $x^1 \in R^N$...