Data-driven constrained optimal model reduction

Giordano Scarciotti, Zhong Ping Jiang, Alessandro Astolfi

Research output: Contribution to journalArticlepeer-review


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 H2 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).

Original languageEnglish (US)
Pages (from-to)68-78
Number of pages11
JournalEuropean Journal of Control
StatePublished - May 2020


  • Data-driven model reduction
  • Model reduction
  • Non-intrusive model reduction
  • Optimal model reduction
  • System identification

ASJC Scopus subject areas

  • General Engineering


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