Vegetation pattern dynamics is a pivotal research domain in ecology, which can reveal the
impact of the non-uniform distribution of vegetation on ecosystem structure and function …

In this paper a review of the results on sparse controls for partial differential equations is
presented. There are two different approaches to the sparsity study of control problems. One …

We introduce the concept of mean-field optimal control which is the rigorous limit process
connecting finite dimensional optimal control problems with ODE constraints modeling multi …

Starting with the seminal papers of Reynolds (1987), Vicsek et al.(1995), Cucker–Smale
(2007), there has been a lot of recent works on models of self-alignment and consensus …

We introduce the rigorous limit process connecting finite dimensional sparse optimal control
problems with ODE constraints, modelling parsimonious interventions on the dynamics of a …

This article is mainly based on the work [7], and it is dedicated to the 60th anniversary of B.
Bonnard, held in Dijon in June 2012. We focus on a controlled Cucker--Smale model in finite …

Optimal control problems in measure spaces lead to controls that have small support, which
is desirable, eg, in the context of optimal actuator placement. For problems governed by …

A directional sparsity framework allowing for measure valued controls in the spatial direction
is proposed for parabolic optimal control problems. It allows for controls which are localized …

Optimal control problems with semilinear parabolic state equations are considered. The
objective features one out of three different terms promoting various spatio-temporal sparsity …

Many applications require minimizing the sum of smooth and nonsmooth functions. For
example, basis pursuit denoising problems in data science require minimizing a measure of …