Ninth Annual Graduate Student Miniconference in Computational Mathematics
Klajdi Sinani
Virginia Tech http://www.math.vt.edu/people.php?type=Graduates&pid=klajdi 

Abstract 
$\mathcal{H} _ 2(t _ f)$ optimality conditions for a finitetime horizon
Simulation, design, and control of largescale dynamical systems play an important role in numerous scientific and industrial tasks. However, largescale dynamical systems pose tremendous computational difficulties when applied in numerical simulations. In order to overcome these challenges we use model reduction. In this paper, we establish necessary $\mathcal{H} _ 2(t _ f)$ optimality conditions for model reduction over a finitetime horizon. In this paper we establish both gramian based optimality conditions on a finite horizon, and interpolation based conditions. We construct an algorithm, called FHIRKA, which yields a reduced model that satisfies the established interpolationbased optimality conditions. 