Near-optimal Frequency-weighted Interpolatory Model Reduction
For control engineers and researchers in model reduction, this provides a more efficient algorithm for weighted-H2 reduction of large-scale MIMO systems.
This paper develops an interpolatory framework for weighted-H2 model reduction of MIMO dynamical systems, deriving first-order necessary conditions for optimality and an algorithm that remains tractable for large state-space dimensions. Numerical examples demonstrate competitiveness with Frequency Weighted Balanced Truncation and the Weighted Iterative Rational Krylov Algorithm.
This paper develops an interpolatory framework for weighted-$\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive associated first-order necessary conditions satisfied by optimal weighted-$\mathcal{H}_2$ reduced-order models. Equivalence of these new interpolatory conditions with earlier Riccati-based conditions given by Halevi is also shown. An examination of realizations for equivalent weighted-$\mathcal{H}_2$ systems leads then to an algorithm that remains tractable for large state-space dimension. Several numerical examples illustrate the effectiveness of this approach and its competitiveness with Frequency Weighted Balanced Truncation and an earlier interpolatory approach, the Weighted Iterative Rational Krylov Algorithm.