CEC Faculty Articles

Title

A Null-Space-Based Technique for the Estimation of Linear-Time Invariant Structured State-Space Representations

Event Date/Location

Brussels, Belgium

Document Type

Article

Date

7-2012

Publication Title

IFAC Proceedings Volumes

ISSN or ISBN

1474-6670

Volume

45

Issue

16

First Page

191

Last Page

196

Description

Estimating the order as well as the matrices of a linear state-space model is now an easy problem to solve. However, it is well-known that the state-space matrices are unique modulo a non-singular similarity transformation matrix. This could have serious consequences if the system being identified is a real physical system. Indeed, if the true model contains physical parameters, then the identified system could no longer have the physical parameters in a form that can be extracted easily. The question addressed in this paper then is, how to recover the physical parameters once the system has been identified in a fully-parameterized form. The novelty of our approach is on transforming the bilinear equations arising from the similarity transformation equations as a null-space problem. We show that the null-space of a certain matrix contains the physical parameters. Extracting the physical parameters then requires the solution of a non-convex optimization problem in a reduced dimensional space. By assuming that the physical state-space form is identifiable and the initial fully-parameterized model is consistent, the solution of this optimization problem is unique. The proposed algorithm is presented, along with an example of a physical system.

DOI

10.3182/20120711-3-BE-2027.00075

This document is currently not available here.

Peer Reviewed

Find in your library

Share

COinS