System identification for a particular approach reduces to system reduction, determining for a system with a high state-space dimension a system of low state-space dimension. For Gaussian systems the problem of system reduction is considered with the divergence rate criterion. The divergence or Kullback-Leibler pseudo-distance corresponds to the expected value of the negative natural logarithm of the likelihood function. System reduction for Gaussian systems is thus a certainty equivalent way of maximum likelihood identification. An algebraic method is proposed for system reduction. The results are a theorem that this problem reduces to an infimization problem for a rational function for which programs are available and a procedure for computing the best approximant w.r.t. the divergence rate criterion. As illustration two examples of system reduction are presented.

Algebraic method, Divergence, Gaussian system, Global optimization, Local minima, Maximum likelihood method, System identification, System reduction
dx.doi.org/10.1016/S1474-6670(17)35034-6
IFAC Symposium on System Identification
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Jibetean, D, & van Schuppen, J.H. (2003). An algebraic method for system reduction of stationary Gaussian systems. In IFAC-PapersOnLine (pp. 1879–1884). doi:10.1016/S1474-6670(17)35034-6