Model reduction by moment matching can be interpreted as the problem of finding a reduced-order model which possesses the same steady-state output response of a given full-order system for a prescribed class of input signals. Little information regarding the transient behavior of the system is systematically preserved, limiting the use of reduced-order models in control applications. In this paper we formulate and solve the problem of constrained optimal model reduction. Using a data-driven approach we determine an estimate of the moments and of the transient response of a possibly unknown system. Consequently we determine a reduced-order model which matches the estimated moments at the prescribed interpolation signals and, simultaneously, possesses the estimated transient. We show that the resulting system is a solution of the constrained optimal model reduction problem. Detailed results are obtained when the optimality criterion is formulated with the time-domain ℓ₁, ℓ₂, ℓ_∞ norms and with the frequency-domain ${\mathcal{H}}_2$ norm. The paper is illustrated by two examples: the reduction of the model of the vibrations of a building and the reduction of the Eady model (an atmospheric storm track model).

通过矩量匹配进行的模型简化可以解释为以下问题：找到一个降阶模型，该模型对于指定的输入信号类别，具有与给定全阶系统相同的稳态输出响应。关于系统瞬态行为的信息很少被系统地保留，从而限制了降阶模型在控制应用中的使用。本文我们制定并解决了约束问题最佳模型简化。使用数据驱动的方法，我们可以确定可能未知系统的力矩和瞬态响应的估计值。因此，我们确定了一个降阶模型，该模型与指定插值信号处的估计矩匹配，并且同时具有估计的瞬态。我们证明了所得系统是约束最优模型简化问题的一种解决方案。当最优性准则的配制与时域ℓ得到详细的结果₁，ℓ ₂，ℓ _∞准则和与频域${\mathcal{H}}_2$规范。本文通过两个示例进行说明：减少建筑物振动模型和减少Eady模型（大气风暴轨迹模型）。