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arXiv · 1806.10797

$\mathcal{H}_2(t_f)$ Optimality Conditions for a Finite-time Horizon

Klajdi Sinani·Serkan Gugercin
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Abstract

In this paper we establish the interpolatory model reduction framework for optimal approximation of MIMO dynamical systems with respect to the $\mathcal{H}_2$ norm over a finite-time horizon, denoted as the $\mathcal{H}_2(t_f)$ norm. Using the underlying inner product space, we derive the interpolatory first-order necessary optimality conditions for approximation in the $\mathcal{H}_2(t_f)$ norm. Then, we develop an algorithm, which yields a locally optimal reduced model that satisfies the established interpolation-based optimality conditions. We test the algorithm on various numerical examples to illustrate its performance.

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Klajdi Sinani, Serkan Gugercin. 2018-06-28. $\mathcal{H}_2(t_f)$ Optimality Conditions for a Finite-time Horizon. https://arxiv.org/abs/1806.10797

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