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.

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

Sincronization of coupled oscillator described by the Kuramoto model, using the Stochastic Conjugate Gradient Method

In this work, we address the optimal control of parameter-dependent systems.

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...

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.

We analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian $(-\Delta)^s$ ($0 < s < 1 $) on the interval $(-1,1)$. We prove the existence of a minimal (strictly positive) time $T_{\rm min}$ such that the fractional heat dynamics can be controlled from any initial datum in $L^2(-1,1)$ to a positive trajectory through the action of a positive control, when $s>1/2$. Moreover, we show that in this minimal time constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. We also give some numerical simulations that confirm our theoretical results.

Using IpOpt to get the time-optimal nonnegative control of a semi-discrete 1D heat equation

The aim of this work is to recover the initial sparse sources that lead to a given final measurements using the diffusion equation. It is assumed that the initial condition can be written down as a linear combination of unitary deltas and their weights. In that context, an algorithm that combines the adjoint methodology with least squares is presented. In particular, the adjoint methodology is used to find the localization of the sparse sources and least squares to find the corresponding intensities.

Autonomous Vehicles (briefly AVs) have already been tested on urban and highway networks and, for the future they may be used to monitor and manage the vehicular traffic. The impact of autonomous vehicles on vehicular traffic is modeled by a PDE+ODE models with moving point-flux constraint. The PDE is a nonlinear hyperbolic conservation laws and the ODE represents the trajectory of autonomous vehicles. We show that the data collected by autonomous vehicles' sensors can be used to reconstruct the traffic state.

Various discrete adjoint methodologies are discussed for the inverse design of linear transport equations in 2 space dimensions

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.

We describe a FE method for the approximation of the one-dimensional fractional Laplacian $(-d_x^2)^s$ on a uniform mesh discretizing the symmetric interval $(-L,L)$, $L>0$.

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.

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

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