The Module Structure of ARMAX Systems

Author

Markovsky, Ivan ; Willems, Jan C. ; Moor, Bart De

Author_Institution

Electr. Eng. Dept., Katholieke Univ., Leuven

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

811

Lastpage

816

Abstract

We consider ARMAX system representations and identification problems. Identifiability conditions in terms of the correlation function of the process are given. One of the conditions is persistency of excitation of an input component of the process and another one is a rank condition for a pair of Hankel matrices. We study the linear combinations of the process and its shifts that produce a process independent of the input. The set of all such linear combinations, called the orthogonalizers, has a module structure and under identifiability conditions completely specifies the deterministic part of the ARMAX system. Computing a module basis for the orthogonalizers is a deterministic identification problem. We propose an ARMAX identification algorithm, which has three steps: first compute the deterministic part of the system via the orthogonalizers, then the AR part, which also has a module structure, and finally the MA part

Keywords

autoregressive moving average processes; identification; ARMAX identification algorithm; ARMAX system representations; ARMAX systems; annihilators; correlation function; deterministic identification problem; module structure; orthogonalizers; system identification; Control systems; Difference equations; Polynomials; Stochastic processes; Stochastic systems; System identification; USA Councils; ARMAX representation; System identification; annihilators; module structure; orthogonalizers;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377656

Filename

4177205