CCE Faculty Articles
A Null-Space-Based Technique for the Estimation of Linear-Time Invariant Structured State-Space Representations
Document Type
Article
Publication Title
IFAC Proceedings Volumes
Event Date/Location
Brussels, Belgium
ISSN
1474-6670
Publication Date
7-2012
Abstract
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
Volume
45
Issue
16
First Page
191
Last Page
196
NSUWorks Citation
Ramos, Jose A.; Prot, Olivier; and Mercere, Guillaume, "A Null-Space-Based Technique for the Estimation of Linear-Time Invariant Structured State-Space Representations" (2012). CCE Faculty Articles. 408.
https://nsuworks.nova.edu/gscis_facarticles/408
