TY - JOUR
T1 - Data-driven constrained optimal model reduction
AU - Scarciotti, Giordano
AU - Jiang, Zhong Ping
AU - Astolfi, Alessandro
N1 - Funding Information:
The work of G. Scarciotti has been supported in part by Imperial College London under the Junior Research Fellowship Scheme. The work of A. Astolfi has been supported in part by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement No 739551 (KIOS CoE). The work of Z.P. Jiang has been supported in part by the National Science Foundation under Grant ECCS-1501044 .
Funding Information:
The work of G. Scarciotti has been supported in part by Imperial College London under the Junior Research Fellowship Scheme. The work of A. Astolfi has been supported in part by the European Union's Horizon 2020 Research and Innovation Programme under grant agreement No 739551 (KIOS CoE). The work of Z.P. Jiang has been supported in part by the National Science Foundation under Grant ECCS-1501044.
Publisher Copyright:
© 2019 European Control Association
PY - 2020/5
Y1 - 2020/5
N2 - 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).
AB - 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).
KW - Data-driven model reduction
KW - Model reduction
KW - Non-intrusive model reduction
KW - Optimal model reduction
KW - System identification
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U2 - 10.1016/j.ejcon.2019.10.006
DO - 10.1016/j.ejcon.2019.10.006
M3 - Article
AN - SCOPUS:85075533398
SN - 0947-3580
VL - 53
SP - 68
EP - 78
JO - European Journal of Control
JF - European Journal of Control
ER -