Comparison of a gradient-based algorithm and a proximity control algorithm for gray-box LTI model identification

In this paper, the challenging problem of determining the unknown parameters of an identifiable LTI statespace representation of a stable system is addressed by resorting to a specific H
_∞
-norm-based optimization algorithm. More specifically, by assuming the availability of a reliable fully-parameterized representation of the system to identify, the algorithm developed herein consists in restructuring this initial black-box representation of the system dynamics via the optimization of a dedicated maximum eigenvalue-based criterion. This study shows that this H
_∞
-norm-based approach can be seen as a good solution for the estimation of gray-box LTI state-space forms and, by extension, as an interesting alternative or a reliable initialization step for the standard output-error techniques.