Learning Complexity Dimensions for a Continuous-Time Control System. Kuusela, P.; Ocone, D.; and Sontag, E. SIAM J. Control Optim., 43(3):872–898, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2004.
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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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