**Domènec Ruiz** is a PhD Student at Universidad Autónoma de Madrid (UAM). He earned a BSc in Mathematics and a BSc in Physics at the Universitat Autònoma de Barcelona. Later he earned and a MSc in Applied Mathematics in an Erasmus Mundus program between the Università degli Studi dell'Aquila (UAQ) and Universität Hamburg (UH). His master thesis was about asymptotic analysis and control of kinetic Cucker-Smale models. Currently, he is studying for a PhD in Control Theory under the supervision of Professor Enrique Zuazua.

#### Author's contribution:

#### Control of reaction-diffusion under state constraints - Heterogeneous setting: Gene-flow.

This tutorial is part of the control under state constraints. We will present the main features regarding the controllability of bistable reaction-diffusion equations with heterogeneous drifts.

#### Control of reaction-diffusion under state constraints - Numerical exploration of controls

This tutorial is part of the control under state constraints. We will simulate different control strategies to the same target by minimizing different functionals.

#### Control of reaction-diffusion under state constraints - Application of the staircase method

In this tutorial, we will present how to generate admissible paths of steady states for the homogeneous reaction-diffusion equation

#### Control of reaction-diffusion under state constraints - Barriers

This tutorial is part of the control under state constraints. We will show how obstructions to the state constraint controllability can appear.

#### Control of reaction-diffusion under state constraints

Usually, the unknowns in reaction-diffusion models are positive by nature. Therefore, for application purposes, any control strategy proposed should preserve this positivity. This group of tutorials is devoted to the understanding of phenomena and techniques arising in reaction-diffusion control problems when state constraints are present.

#### Control for a semilinear heat equation and analogies with a collective behavior model

In this tutorial we will apply the DyCon toolbox to find a control to the semi-discrete semi-linear heat equation.

#### Stabilization of a collective behavior model

Summary of example objective The goal of this tutorial is to use LQR theory applied to a model of collective behavior. The model chosen shares a formal structure with the semidiscretization of the semilinear 1d heat equation.