One of the main outputs of the research conducted within DyCon ERC Project is the development of new computational methods and tools (algorithms, tutorials, sample codes, software, simulations, and so on), all of which are constantly being integrated in our computational platform.

DyCon Blog offers a higher layer of the computational platform, gathering the work that is currently taking place inside the DyCon team. The goal of this computational blog is to share the valuable knowledge that was collected and gained throughout the DyCon ERC Project's life cycle.

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 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 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.

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.

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