IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Klajdi Sinani
Virginia Tech
## $\mathcal{H} _ 2(t _ f)$ optimality conditions for a finite-time horizon
Simulation, design, and control of large-scale dynamical systems play an important role in numerous scientific and industrial tasks. However, large-scale 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 finite-time horizon. In this paper we establish both gramian based optimality conditions on a finite horizon, and interpolation based conditions. We construct an algorithm, called FH-IRKA, which yields a reduced model that satisfies the established interpolation-based optimality conditions.