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 in which the quantity of interest is the average of the states with respect to the parameter family $\mathcal{K}= \left\{ \nu_i \in \mathbb{R}, \enspace 1\leq…

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 the control of the wave equation with Matlab. Features With wave control you can explore the following: Exact control of the 1-d wave equation with…

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{equation} \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\ ), \qd t>0, x\in[0,2\pi], v\in \mathbb{R}, \label{eq: VPFP}\\ f(0, x,v,z) = f_0(x,v,z), \qd z\in [a,b]. \end{cases} \end{equation} In the numerical experiments, we compare the results…

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 [latex] \begin{equation}\label{heat_intro} \begin{cases} y_{t}-\textnormal{div}(a(x,\nu)\nabla y) +c\, y=\chi_\omega u \quad &\text{in } Q=\Omega\times(0,T), \\ y=0 \quad &\text{on } \Sigma=\partial\Omega\times(0,T), \\ y(x,0)=y^0(x) \quad&\text{in } \Omega, \end{cases} \end{equation} [/latex]…