Mathematical content not related to the Work Packages of the DyCon ERC Project.

#### Available tutorials:

#### A reaction-diffusion equation with delay

The aim of this tutorial is to give a numerical method for solving a partial differential equation with a constant delay.

#### Structured deformations of continua

A Multiscale Geometrical Basis for Variational Problems in Mechanics

#### The Dirichlet-Neumann iteration for two coupled heterogeneous heat equations

This tutorial explains how to use the Dirichlet-Neumann method to coordinate the numerical solutions of two linear heat equations with strong jumps in the material coefficients accross a common interface.

#### An introduction to the moment method for optimal control problems for polynomial ODEs

The aim of this note is to explain how one can solve an optimal control problem with the moment method

#### Optimal control for inverted pendulum

Tutorial of optimal control for inverted pendulum with symbolic MATLAB

#### Stability analysis of Power Electronic Converters Connected to AC Grids

Stability analysis of a simplified model for Power Electronic Converters Connected to AC Grids in dependence on the characteristical physical parameters.

#### LQR controller for stabilizing the linear population dynamics model

In this tutorial, we will demonstrate how to design a LQR controller in order to stabilize the linear population dynamics model dependent on age and space

#### The control on the Kuramoto model by handling one oscillator

We design the LQR controller and solve it with linearized model.

#### 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 choosen shares a formal structure with the semidiscretization of the semilinear 1d heat equation.

#### Optimal control of a graph evolving in discrete time

Stabilizing the graph by minimizing a discrete LQR and driving it to a reference state.

#### Radial Basis Functions Interpolation

This is a set of Matlab functions to interpolate scattered data with Radial Basis Functions (RBF).