Near Optimal Interpolation based Time-Limited Model Order Reduction

TL;DR

This paper introduces LT-IRKA, an interpolatory algorithm for near optimal time-limited $H_2$ model reduction of LTI systems, achieving high fidelity over finite time intervals.

Contribution

The paper develops a new interpolatory framework, LT-IRKA, for time-limited $H_2$ optimal model reduction, providing near optimal reduced models over finite time horizons.

Findings

LT-IRKA nearly satisfies time-limited optimality conditions.

It outperforms or matches existing algorithms like TL-TSIA, TL-BT, IRKA, and TL-PORK in numerical tests.

Abstract

This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time intervals of the form, $\begin{bmatrix}0 & \tau \end{bmatrix}$ with $\tau < \infty$ for linear time invariant (LTI) systems. Using the time limited $H_2$ norm, we derive interpolation based $H_{2,\tau}$ optimality conditions. The LT-IRKA yields a near optimal $H_2(\tau)$ reduced order system. The nearness to the exact $H_2(\tau)$ optimal reduced system is quantized in terms of the errors in the interpolation based $H_2(\tau)$ optimality conditions. We demonstrate with numerical examples how the proposed algorithm nearly satisfies the time-limited optimality conditions and also how it performs with respect to the Time-Limited Two sided Iteration Algorithm (TL-TSIA), the Time-Limited Balanced Truncation (TL-BT), the Iterative Rational Krylov Algorithm (IRKA) and the Time-Limited Pseudo Optimal Rational Krylov (TL-PORK) Algorithm over a finite time interval.