© The Institution of Electrical Engineers
A method based on the matrix pseudoinverse is presented for the online identification of discrete-time systems of known order. Recursive algorithms are described which provide minimum-norm estimates of the parameter vector when insufficient data are available, and least-squares estimates with adequate data. These estimates can be updated easily with each pair of additional input-output data, as matrix inversion is not required. When the order of the system is not known, it may be determined offline using one of the two methods described. A recursive algorithm for calculating the residual error is also derived. A number of examples are given to illustrate the usefulness of the methods.
References
-
-
1)
-
F.W. Smith
.
System Laplace-transform estimation from sampled data.
IEEE Trans.
,
37 -
44
-
2)
-
A.V. Balakrishnan ,
V. Peterka
.
Identification in automatic control systems.
Automatica
,
817 -
829
-
3)
-
T.N.E. Greville
.
Some applications of the pseudoinverse of a matrix.
SIAM Rev.
,
15 -
22
-
4)
-
R. JOHANSSON
.
(1993)
, System modelling and identification.
-
5)
-
R. Penrose
.
On best approximate solution of linear matrix equations.
Proc. Cambridge Phil. Soc.
,
17 -
19
-
6)
-
A. Albert ,
R.W. Sittler
.
A method for computing least square estimates that keep up with the data.
SIAM J. Control
,
384 -
417
-
7)
-
A.I. Liff
.
System identification in the presence of noise by digital techniques.
IEEE Internat. Conv. Rec.
,
6 ,
152 -
166
-
8)
-
Lee, R.C.K.: `Optimal estimation, identification and control', 28, Research monograph, 1964.
-
9)
-
C.H. Wells
.
Minimum norm control of discrete systems.
IEEE Internat. Conv. Rec.
,
3 ,
55 -
64
http://iet.metastore.ingenta.com/content/journals/10.1049/piee.1971.0207
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