$\mathcal{H}_2(t_f)$ Optimality Conditions for a Finite-time Horizon
For control theorists and engineers, this extends H2 optimal model reduction to finite-time horizons, but the contribution is incremental as it adapts existing interpolation-based methods.
The paper establishes interpolatory optimality conditions for model reduction in the finite-time horizon H2 norm and develops an algorithm that yields locally optimal reduced models satisfying these conditions, with numerical validation.
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.