Time-limited H2-optimal model order reduction

摘要

In this paper, we investigate a time-limited H2-model order reduction method for linear dynamical systems. For this, we propose a time-limited H2-norm and show its connection with the time-limited Gramians. We then derive first-order conditions for optimality of reduced-order systems with respect to the time-limited H2-norm. Based on these optimality conditions, we propose an iterative correction scheme to construct reduced-order systems, which, upon convergence, nearly satisfy these conditions. Furthermore, a diagnostic measure is proposed for how close the obtained reduced-order system is to optimality. We test the efficiency of the proposed iterative scheme using various numerical examples and illustrate that the newly proposed iterative method can lead to a better reduced-order models compared to the unrestricted iterative rational Krylov subspace algorithm in a finite time interval of interest.