In this short tutorial we explain how to use IpOpt in order to solve time optimal control problems. We refer to previous works for a survey on numerical methods in optimal control and how to implement them efficiently according to the context…

#### Greedy Control

Control of a parameter dependent system in a robust manner. Fix a control time , an arbitrary initial data , and a final target …

#### 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…

#### 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…

#### 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…

#### 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…

#### 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…

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

We want to study the following optimal control problem:

#### 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.