Here you will find the whole list of guides and tutorials developed by the DyCon ERC Project's research team and visitors. All of the content has been classified according to the project’s Work Packages.

In this tutorial we will present a simultaneous control problem in a linear system dependent on parameters. We will use the MATLAb DyCon Toolbox library.

In this blog post, we consider a double pendulum on a cart and we solve the problem of swinging up the pendulum from the downward position to the upward position using optimal control techniques.

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

Formulation of Optimal control problem for rotor imbalance. Explanation of the code to numerically solve the problem.

In this short tutorial, we explain how to use Riccati’s theory to solve an LQ control problem with targets.

We want to study the following optimal control problem...

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

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

In this tutorial, we will present and elaborate an optimal control strategy for the obstacle problem in two space dimensions using Python's FEniCS toolbox. Different meshes and obstacles are considered.

A short python implementation of POD and DMD for a 2D Burgers equation using FEniCS and Scipy

The inverse design of hyperbolic transport equations can be addressed by using gradient-adjoint methodologies. Recently, Morales-Hernandez and Zuazua [1] investigated the convenience of using low order numerical schemes for the adjoint resolution in the gradient-adjoint method. They focused on hyperbolic transport scalar equations with an heterogeneous time-independent vector field.

Our aim is to study an optimal control problem which consists in minimizing the difference between the predictions of the Burgers equation and the observations of the system at a final time in $L^2(\mathbb{R})$ norm.

In this tutorial, we present an optimal control problem related to the Fokker-Planck equation.

In this tutorial, we propose the Hum method to approximate numerically the control in a null controllability problem for a non linear population dynamics model structuring in age and spatial diffusion.

In this tutorial, we investigate the linear infinite dimensional system obtained by implementing an age structure to a given linear dynamical system. We show that if the initial system is null controllable in a time small enough, then the age structured system is also null controllable in a time depending on the various involved parameters.

In this DyCon Toolbox tutorial, we present how to use OptimaControl enviroment to control a consensus that models the complex emergent dynamics over a given network.

The aim of this work is to use CasADi and IpOpt to simulate optimal control problem, which explains the structural controllability of the 2D heat equation. We use finite difference scheme with the uniform grid to test exact controllability of the 2D heat equation. After that, we delete several interactions between grid points and simulate the controllability with smaller number of controlled points.

In this post, we use IpOpt and AMPL to simulate optimal controls on a nonlinear ODE system with unbounded interactions. The restriction and initial guess on the state variables are critical for this problem to operate minimization algorithm. From the data calculated from AMPL, we interpret and visualize it using Matlab.

Optimal Control in OpenFOAM

Tutorial of optimal control for inverted pendulum with symbolic MATLAB

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

Design of a LQR controller for the stabilization of a fractional reaction diffusion equation

In this tutorial we study the localization of touchdown points in a mathematical model for micro-electro-mechanical systems (MEMS) with variable dielectric permittivity. We consider a device consisting of two conducting plates, connected to an electric circuit. The upper plate is rigid and fixed while the lower one is elastic and fixed only at the boundary. When a voltage (difference of potential between the two plates) is applied, the lower plate starts to bend and, if the voltage is large enough, the lower plate eventually touches the upper one. This is called touchdown phenomenon and our aim is to control the localization of touchdown points in the device by a suitable choice of the dielectric permittivity of the material.

We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes, and we illustrate that numerical solutions may have unexpected behaviours with respect to the analytic ones.

A Multiscale Geometrical Basis for Variational Problems in Mechanics