## The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term

Shi Jin, Yuhua Zhu, Enrique Zuazua. The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term Numer. Math. 150, 479–519 (2022). https://doi.org/10.1007/s00211-021-01257-w Abstract. We consider the Vlasov-Fokker-Planck equation with random electric…

## Local null controllability of a model system for strong interaction between internal solitary waves

Jon Asier Bárcena-Petisco, Sergio Guerrero and Ademir F. Pazoto.  Local null controllability of a model system for strong interaction between internal solitary waves. Commun. Contemp. Math. (2021) https://doi.org/10.1142/S0219199721500036 Abstract. In…

## DyCon blog: Averaged dynamics and control for heat equations with random diffusion

Spain. 04.12.2020. Our team member Jon Asier Bárcena Petisco and our Head Enrique Zuazua made a contribution to the DyCon Blog about "Averaged dynamics and control for heat equations with…

## Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions

J.-C. Cortes, A. Navarro-Quiles, J.-V. Romero, M.-D. Rosello, E. Zuazua. Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions. J. Franklin I. (2020)…

## Averaged Control

PDF version | Download Matlab Code | Download Scilab Code | GITHUB In this work, we address the optimal control of parameter-dependent systems. We introduce the notion of averaged control…

## Wavecontrol

Manual PDF   |   Download Code... A Matlab guide for the numerical approximation of the exact control and stabilization of the wave equation This webpage contains a free software to compute…

## Greedy algorithm for Parametric Vlasov-Fokker-Planck System

PDF version...  |   Download Code... 1. Numerical experiments Consider the one dimensional linear Vlasov-Fokker-Planck (VPFP) as following. \begin{cases} \delta\pt_tf + \sigma_1v\delta\pt_x f - \frac{\sigma_2}{\epsilon} \delta\pt_x\phi\delta\pt_v f =\frac{\sigma_3}{\epsilon}\delta\pt_v\ (v f +\delta\pt_vf\…

## Greedy optimal control for elliptic problems and its application to turnpike problems

PDF version  |   Download Code... 1. Problem formulation Let $\Omega\subset \mathbb R^d$ be an open and bounded Lipschitz Domain and consider the parameter dependent parabolic equation with Dirichlet boundary conditions where…

## Greedy Control

Control of a parameter dependent system in a robust manner. Fix a control time $T > 0$, an arbitrary initial data $x^0$, and a final target $x^1 \in R^N$...

## Control of parameter dependent problems (PDC)

In real applications, models are not completely known since relevant parameters (deterministic or stochastic) are subject to uncertainty and indetermination. Accordingly, for practical purposes, robust analytical and computational methods are…