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 work we address the optimal control of parameter-dependent systems. In particular, we study the dynamics and averaged controllability properties of heat equations with random non-negative diffusivites.

Simultaneous control of parameter-depending systems using stochastic optimization algorithms

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.

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.

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

In this tutorial we study the inverse design problem for time-evolution Hamilton-Jacobi equations. More precisely, for a given observation of the viscosity solution at time $T>0$, we construct all the possible initial data that could have led the solution to the observed state. We note that these initial data are not in general unique.

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

Numerical implementation of the moving control strategy for a two dimensional heat equation with memory

In this tutorial, we show the simulation of heat fractional equation

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.

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

In this tutorial we show how to implement the Q-learning algorithm in simple settings where the state-space and the control-space are finite. In this case, the Q-function can be represented by a table, and therefore, it belongs to a finite-dimensional vector space. We illustrate the algorithm by solving the problem of finding the shortest path between any arbitrary point in a discretized domain and a target area. We then consider the same problem in a domain affected by a potential.

Tutorial of optimal control for inverted pendulum with symbolic MATLAB