** | Download Code** related to the Kolmogorov Equation problem.

**Developed by Mehmet Ersoy & Enrique Zuazua**.

#### Solving an optimal control problem arised in ecology with AMPL

PDF version… Introduction We are interested in optimal control problems subject to a class of diffusion-reaction systems that describes the growth and spread of an introduced population of organisms (1) where (2) is the reaction term that represents local reactions, and is the state of the system. Here and are two real parameters.…

#### Kolmogorov equation

PDF version… | Download Code… | 1 Introduction We are interested in the numerical discretization of the Kolmogorov equation [12] (1) where is a diffusive function and a potential function. This is one example of degenerate advection-diffusion equations which have the property of hypo-ellipticity (see for instance, [6, 13, 14]), ensuring the regularity of solutions for…

#### 2D inverse design of linear transport equations on unstructured grids

PDF version… 1. Adjoint estimation: low or high order? Adjoint methods have been systematically associated to the optimal control design [5] and their applications to aerodynamics [1, 4]. During the last decades, several works were oriented to develop a robust control theory based on the concepts of observability, optimality and controllability for linear and non-linear…

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

PDF version… 1. Problem formulation Let be an open and bounded Lipschitz Domain and consider the parameter dependent parabolic equation with Dirichlet boundary conditions (1) where is the state, is a control function and is given initial datum. In (1), is a scalar coefficient depending on some parameter and is given. To abridge the…

#### IpOpt and AMPL use to solve time optimal control problems

PDF version… | Download Code… | Featured Video Evolution of the controls and of the state for , , and the discretization parameters , in the minimal computed time . Your browser does not support the video tag. Introduction In this short tutorial we explain how to use IpOpt in order to solve time optimal control problems.…

#### Poisson Equation Numerical Control MATLAB code

** | Download Code** related to Finite element approximation of the 1-D fractional Poisson equation.

**Developed by Umberto Biccari, Víctor Hernández-Santamaría & Enrique Zuazua**

#### Finite element approximation of the 1-D fractional Poisson equation

A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control.

#### Turnpike property for functionals involving L^{1}−norm

We want to study the following optimal control problem:

#### Conservation laws in the presence of shocks

PDF version… The problem We analyze a model tracking problem for a 1D scalar conservation law. It consists in optimizing the initial datum so to minimize a weighted distance to a given target during a given finite time horizon. To be more precise, given a finite time , a target function , and a positive…