# Observability for Initial Value Problems with Sparse Initial Data - Mathematics > Optimization and Control

Abstract: In this work we introduce the concept of $s$-sparse observability for largesystems of ordinary differential equations. Let $\dot x=ft,x$ be such asystem. At time $T>0$, suppose we make a set of observations $b=AxT$ of thesolution of the system with initial data $x0=x^0$, where $A$ is a matrixsatisfying the restricted isometry property. The aim of this paper is to giveanswers to the following questions: Given the observations $b$, is $x^0$uniquely determined knowing that $x^0$ is sufficiently sparse? Is there any wayto reconstruct such a sparse initial data $x^0$?

Author: Nicolae Tarfulea

Source: https://arxiv.org/