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.

The Multilevel Selective Harmonic Modulation problem is recast under the perspective of optimal control

The aim is then to open the black box of Deep Learning, and try to gain an intuition of what are these models doing. One of the most succesful mathematical theories in recent years has been connecting Deep Learning with Dynamical Systems.

In this project we tried first working on finding an algorithm that can help us define the points of interest of the users we have in the dataset. For that we implement an algorithm that can identify the users stop points.

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.

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.

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

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.