Home > System Identification > 14th IFAC Symposium on System Identification, 2006 > A kernel based approach to structured nonlinear system identification part I: Algorithms
A kernel based approach to structured nonlinear system identification part I: Algorithms
System Identification, Volume # 14 | Part# 1
Location: , Australia
National Organizing Committee Chair: Brett Ninness,
Håkan Hjalmarsson
International Program Committee Chair: Iven Mareels
Conference Editor: Brett Ninness,
Håkan Hjalmarsson
Authors
Kenneth Hsu; Tyrone Vincent; Kameshwar Poolla
Identifier
10.3182/20060329-3-AU-2901.00193
Index Terms
nonlinear system identification,structured systems,kernel
Abstract
We consider interconnected systems consisting of linear time-invariant systems and static nonlinear maps. Under the assumptions that the linear dynamics are known and the input to the nonlinear maps are measurable, it is shown that the identification problem can be reduced to a least squares problem. An identification algorithm utilizing a kernel-based dispersion function is proposed.
References
[1] Barron, A. R. (1993). Uniform approximation
bounds for superpositions of a sigmoidal function.
IEEE Transactions on Information Theory
39, 930-945.
[2] Claassen, M. (2001). System identification for
structured nonlinear systems. Ph.D. Dissertation,
University of California at Berkeley.
[3] Greblicki, W. (1989). Nonparametric orthogonal
series identification of hammerstein systems.
International Journal of Systems Science
20, 2355-2367.
[4] Greblicki, W. (1997). Nonparametric approach to
wiener system identification. IEEE Transactions
on Circuits and Systems 44, 538-545.
[5] Hsu, K., C. Novara, M. Milanese and K. Poolla
(2005a). Parametric identification of static
nonlinearities in a general interconnected system.
Proceedings of the 16th IFAC World
Congress.
[6] Hsu, K., M. Claassen, C. Novara, P. Khargonekar,
M. Milanese and K. Poolla (2005b). Nonparametric
identification of static nonlinearities in
a general interconnected system. Proceedings
of the 16th IFAC World Congress.
[7] Hsu, K., T. Vincent and K. Poolla (2005c). A
kernel based approach to structured non-linear
system identification part II: Convergence
and consistency. Proceedings of the
2006 IFAC Symposium on System ID.
[8] Hsu, K., T. Vincent, C. Novara, M. Milanese and
K. Poolla (2005d). Identification of nonlinear
maps in interconnected systems. Proceedings
of the 2005 Conference on Decision and Control
.
[9] Juditsky, A., H. Hjalmarsson, A. Benveniste,
B. Delyon, L. Ljung, J. Sjöberg and Q. Zhang
(1995). Nonlinear black-box models in system
identification: Mathematical foundations.
Automatica 31, 1725-1750.
[10] Kailath, T., A. Sayed and B. Hassibi (2000). Linear
Estimation. Prentice Hall. Upper Saddle
River, New Jersey.
[11] Kryzak, A. (1989). Identification of discrete hammerstein
systems by the fourier series regression
estimate. International Journal of Systems
Science 20, 1729-1744.
[12] Ljung, L. (1999). System Identification Theory for
the User, 2nd Edition. Prentice Hall. Upper
Saddle River, N.J.
[13] Schölkopf, B. and A. J. Smola (2002). Learning
with Kernels. MIT Press. Cambridge.
[14] Sjöberg, J., Q. Zhang, L. Ljung, A. Benveniste,
B. Delyon, P. Y. Glorennec, H. Hjalmarsson
and A. Juditsdy (1995). Nonlinear black-box
modeling in system identification: A unified
overview. Automatica 31, 1691-1724.
[15] Wemhoff, E. (2003). Signal estimation in structured
nonlinear systems with unknown functions.
Ph.D. Dissertation, University of California
at Berkeley.
[16] Wemhoff, E., A. Packard and K. Poolla (1999).
On the identification of nonlinear maps in a
general interconnected system. Proceedings of
the 1999 American Controls Conference.
