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

The DyCon Blog offers a higher layer of our computational platform, bringing together the work done by our team. The objective of this computational blog is to share the knowledge that was collected and obtained throughout the life cycle of the DyCon ERC Project.

Simultaneous control of parameter-depending systems using stochastic optimization algorithms

Deep supervised learning roughly consists in solving a discretised optimal control problem subject to a nonlinear, discrete-time dynamical system, called an artificial neural network.

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.

In this tutorial, we will present how to generate admissible paths of steady states for the homogeneous reaction-diffusion 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 present a simultaneous control problem in a linear system dependent on parameters. We will use the MATLAb DyCon Toolbox library.

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

Usually, the unknowns in reaction-diffusion models are positive by nature. Therefore, for application purposes, any control strategy proposed should preserve this positivity. This group of tutorials is devoted to the understanding of phenomena and techniques arising in reaction-diffusion control problems when state constraints are present.

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

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.

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.