Learning Complexity Dimensions for a Continuous-Time Control System. Kuusela, P., Ocone, D., & Sontag, E. SIAM J. Control Optim., 43(3):872–898, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2004. doi abstract bibtex This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no greater than n. The main result establishes that the sample complexity needed for identification scales polynomially with n and logarithmically with k.
@ARTICLE{kuusela_ocone_sontag04,
AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Learning Complexity Dimensions for a Continuous-Time
Control System},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {872--898},
VOLUME = {43},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {theory of computing and complexity, VC dimension},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/kuusela-ocone-sontag-as-published-SIAM04.pdf},
ABSTRACT = { This paper takes a computational learning theory
approach to a problem of linear systems identification. It is assumed
that input signals have only a finite number k of frequency
components, and systems to be identified have dimension no greater
than n. The main result establishes that the sample complexity needed
for identification scales polynomially with n and logarithmically
with k. },
DOI = {http://dx.doi.org/10.1137/S0363012901384302}
}
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