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Finite Time Identification in Unstable Linear Systems. (arXiv:1710.01852v1 [cs.SY])
来源于:arXiv
Identification of the parameters of stable linear dynamical systems is a
well-studied problem in the literature, both in the low and high-dimensional
settings. However, there are hardly any results for the unstable case,
especially regarding finite time bounds. For this setting, classical results on
least-squares estimation of the dynamics parameters are not applicable and
therefore new concepts and technical approaches need to be developed to address
the issue. Unstable linear systems reflect key real applications in control
theory, econometrics, and finance.
This study establishes finite time bounds for the identification error of the
least-squares estimates for a fairly large class of heavy-tailed noise
distributions, and transition matrices of such systems. The results relate the
time length required as a function of the problem dimension and key
characteristics of the true underlying transition matrix and the noise
distribution. To obtain them, appropriate concentration inequaliti 查看全文>>