DyCon Blog

Multilevel Selective Harmonic Modulation via Optimal Control

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

Authors: Jesus Oroya, Carlos Esteve, Umberto Biccari - 25 March 2021

Opening the black box of Deep Learning

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.

Author: Sergi Andreu - 22 March 2021

Points of Interest Extraction and Prediction of Next Locations

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.

Author: Aicha Karite - 10 March 2021

Averaged dynamics and control for heat equations with random diffusion

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.

Author: Jon Asier Bárcena-Petisco - 23 November 2020

Q-learning for finite-dimensional problems

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.

Author: Carlos Esteve - 22 October 2020

Moving control strategy for memory-type equations

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

Authors: Jesus Oroya, Umberto Biccari - 20 October 2020

Stochastic optimization for simultaneous control

Simultaneous control of parameter-depending systems using stochastic optimization algorithms

Authors: Ana Navarro, Umberto Biccari, Enrique Zuazua - 03 June 2020

Synchronized Oscillators

Synchronization of coupled oscillators with the Random Batch Method

Authors: Umberto Biccari, Enrique Zuazua - 03 June 2020

The interplay of control and deep learning

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.

Author: Borjan Geshkovski - 30 April 2020

Control of reaction-diffusion under state constraints - Heterogeneous setting: Gene-flow.

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.

Authors: Domenec Ruiz, Idriss Mazari - 19 April 2020

Control of reaction-diffusion under state constraints - Numerical exploration of controls

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

Author: Domenec Ruiz - 04 April 2020

Inverse problem for Hamilton-Jacobi equations

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.

Author: Carlos Esteve - 03 April 2020

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