Bounding uncertainty in subspace identification

Project members: T.J.J. van den Boom, V. Verdult, B.R.J. Haverkamp

In this project we aim at the estimation of the uncertainty on models, identified using subspace identification methods.

In the recent years, subspace model identification (SMI) has become a popular tool for the identification of state-space models under the influence of disturbances. The fully parameterized state-space is estimated using robust and accurate subspace model identification methods, such as CVA, MOESP and N4SID. They are being used in many different practical applications.

The uncertainty region is specified in a polytopic description. This description is a powerful and elegant way to describe the parametric uncertainty set in the case of state-space models. For plants in an polytopic uncertainty description, robust controller can be designed using optimization techniques based on Linear Matrix Inequalities (LMI). For this type of optimization problems fast and reliable algorithms exist that solves the problem in polynomial time.

The key in this method described in [37] and [38] is the calculation of the first or higher order approximation of the relation between the perturbation on the data and the error on the elements in the identified state-space matrices. Using this approximation one can find a polytopic description of the uncertainty region of the identified model. In a final step, the dimension of the polytopic description can be reduced. All three mentioned subspace identification algorithms (MOESP, N4SID and CVA) can be handled by the above method, since the three algorithms are closely related.