COURSE (pdf)- This is a 10-lecture course of 6 ECTS points. The aim of the course is to provide students with a basic understanding of the techniques common in the area, and an overview of the methods available in the literature.  Additionally, we will focus on a detailed discussion of some selected methods.

The first 3-4 lectures will concern the identification of general nonlinear systems. In addition to a brief introduction of traditional methods, topics that will be covered include the minimum mean squared error estimator,  the direct weight optimization approach, generalized additive nonlinear systems, systems with short term memory and low degree of interactions, the tradeoff between the goodness of fit and model complexity and effects of the noise, and a discussion of the the effect of outliers.

The next 3-4 lectures cover various identification methods for block-oriented nonlinear systems. Examples are decoupling of linear and nonlinear parts, blind identification, a frequency approach, iterative algorithms and others. Identification of Wiener systems using the least amount of a priori information will also be discussed.

The final three lectures are devoted to applications of nonlinear system identification. A number of examples will be used to illustrate concepts, including adaptive bolus chasing angiography, identification of a modified Wiener-Hammerstein system for modeling electrically stimulated paralyzed skeletal muscle behaviors, modeling of a biological cell system and other non-biological, medical applications.

A series of reference papers will be provided to the participants.

Assessment will be based on a written report of a take-home project.

LECTURER - Erwei Bai received his PhD degree from University of California, Berkeley in 1987. He has been with the University of Iowa since then and holds the rank of professor in the Department of Electrical and Computer Engineering and the Department of Radiology. His research interests are in system identification, signal processing and their applications in life science and engineering problems. He is an IEEE Fellow and a recipient of the Presidents Award for Teaching Excellence and the (State of Iowa Board of) Regents Award for Faculty Excellence. He has more than 150 journal publications to his credits.

DATA -Datasets for the final report can be found here.

REFERENCES:

EM

1. •Adrian Wills Thomas B. Schon,  Brett  Ninness , Parameter Estimation for Discrete-Time Nonlinear Systems Using EM, Proceedings of the 17th World Congress, The International Federation of Automatic Control, Seoul, Korea, July 6-11, 2008
   

MCMC

1. •Brett Ninness and Soren Henriksena, Bayesian system identification via Markov chain Monte Carlo techniques, Automatica, Volume 46, Issue 1, January 2010, Pages 40-51
   

Kernel

1. •A Georgiev, IEEE Trans on AC, Vol. 29, NO. 3, pp356-358, 1984
   

2. •EW Bai, R Tempo and Y Liu, Identification of IIR nonlinear systems without prior structural information,IEEE Trans on AC, Vol52, No. 3, 2007
   

Direct weight optimization

1. •Jacob Roll, Alexander Nazin, Lennart Ljung, Nonlinear system identification via direct weight optimization, Automatica, Volume 41, Issue 3, March 2005, Pages 475-490
   

2. •Piecewise linear solution paths with application to direct weight optimization , Automatica, Volume 44, Issue 11, November 2008, Pages 2745-2753
   

3. •EW Bai, Y Liu, Recursive direct weight optimization in nonlinear system identification: a minimal probability approach, IEEE Trans on AC, Vol. 52, No. 7, 2007
   

MMSE estimator

1. •J Fan and I Gijbels, Local polynomial modeling and its applications, Chapman and Hall/CRC, 1996
   

2. •Bai, E.W. “Non-Parametric Nonlinear System Identification: An Asymptotic Minimum Mean Squared Error Estimator”, IEEE Trans on Automatic Control, Vol. 55, No. 7, pp.1615-1626, 2010
   

Short memory and low degree

1. •S.Sperlich, D. Tjostheim and L Yang, Nonparametric estimation and testing of iteraction in additive models, Econometric Theory, Vol. 18, 2002, pp.197-251
   

2. •Bai, E.W., “Identification of additive nonlinear systems”, Automatica, Vol. 41, pp.1247-1253, 2005
   

3. •Bai, E.W. and K.S. Chan, “Identification of an additive nonlinear system and its application in generalized Hammerstein models’’, Automatica, Vol.44, pp.430-436, 2008
   

4. •E.W. Bai, ``Non-Parametric Nonlinear System Identification: a Data-Driven Orthogonal Basis Function Approach’’, IEEE Trans on Automatic Control,  Vol. 53, pp.2615-2626, Dec. 2008
   

5. •Bai EW and M Deistler , "An Interactive Term Representation and Estimation Approach to Non-Parametric FIR Nonlinear System Identification", IEEE Trans on Automatic Control, Vol.55, No.8, pp.1952-1957, 2010
   

6. •Bai,E.W. and R. Tempo, “Representation and Identification of Nonparametric Nonlinear Systems of Short Term Memory and Low Degree of Interactions”, Automatica, Vol. 46, pp.1595-1603,  2010
   

General block oriented system

1. •F. Giri and EW Bai , “Block-oriented Nonlinear System Identification”, F. Giri and EW Bai, Springer, 2010
   

Hammerstein: over parameterization

1. •Chang, F. and R. Luus (1971). A non-iterative method for identification using Hammerstein model. IEEE Trans. Automatic Control, 16, 464-468
   

2. •EW Bai (1998) An optimal two stage identification algorithm for Hammerstein-wiener nonlinear systems, Automatica, Vol. 34, pp333-338
   

Hammerstein: iterative

1. •Narendra, K. S., & Gallman, P. G. (1966). An iterative method for the identification of nonlinear systems using a Hammerstein model. IEEE Transactions on Automatic Control, 11, 546–550.
   

2. •Stoica, P. (1981). On the convergence of an iterative algorithm used for Hammerstein system identification. IEEE Transactions on Automatic Control, 26, 967–969.
   

3. •Rangan, S., G. Wolodkin and K. Poolla (1995). Identification methods for Hammerstein systems. Proc. CDC, New Orleans, 697-702
   

4. •Liu, Y., & Bai, E. W. (2007). Recursive identification of Hammerstein systems. Automatica, 46, 346–354
   

5. •Bai, E. W., & Li, D. (2004). Convergence of the iterative Hammerstein system identification algorithm. IEEE Transactions on Automatic Control, 49, 1929–1940.
   

6. •Bai EW and K Li, (2010) Convergence of the iterative algorithm for a general Hammerstein system identification, Automatica, Vol. 46, pp.1891-1896
   

Hammerstein: blind

1. •Sun, L,w Liu and A sano (1998), Identification of dynamical systems with input nonlinearity, Proc. Inst Elec Eng Control. Theory applicat p41-51
   

2. •Bai, E.W. and Fu, M., “Blind System Identification for IIR Systems, Without Statistical Information”, IEEE Trans. On Signal Processing, June 1999
   

3. •Bai, E.W. and Fu, M., “Blind System Identification for IIR Systems, Without Statistical Information”, IEEE Trans. On Signal Processing, June 1999
   

4. •Bai, E.W., Li, Q. and Dasgupta, S., “Blind Identifiability of IIR Systems,” Automatica, Vol. 38, 2002, pp. 181-184
   

5. •Bai, E.W., “A Blind Approach to Hammerstein-Wiener Model Identification”, Automatica, Vol. 38, 2002, pp. 967-979
   

6. •Bai, EW and Fu, “A Blind Approach to Hammerstein Model Identification”, IEEE Trans. On SP, Vol. 50, 2002, pp. 1610-1619
   

7. •Bai, EW and Fu, “A Blind Approach to Hammerstein Model Identification”, IEEE Trans. On SP, Vol. 50, 2002, pp. 1610-1619.
   

Hammerstein: separable least squares

1. •D. Westwick and R. Kearney, “Separable least squares identification of nonlinear Hammerstein models: application to stretch reflex dynamics,” Ann. Biomed. Eng., vol. 29, pp. 707–718, 2001.
   

2. •Bai, EW (2002) Identification of linear systems with hard input nonlinearities of known structure, Automatica, Volume 38, Issue 5, Pages 853-860
   

Hammerstein: decoupling inputs

1. •Bai, EW, (2004) Decoupling the linear and nonlinear parts in Hammerstein model identification Automatica, Volume 40, Issue 4, Pages 671-676
   

Hammerstein: frequency

1. •Bai, E.W., “A Frequency Domain Approach to Hammerstein Model Identification”, IEEE Trans. on Automatic Control, Vol. 48, 2003, pp. 530-542.
   

2. •S. Baumgartner and W. Rugh, “Complete identification of a class of nonlinear systems from steady state frequency response,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 753–759, Sept. 1975.
   

3. •A. Krzyzak, “On nonparametric estimation of nonlinear dynamic systems by the Fourier series estimate,” Signal Processing, vol. 52, pp. 299–321, 1996.
   

4. •P.Ph. Crama and J. Schoukens, “First estimates ofWiener and Hammerstein systems using multisine excitation,” in Proc. IEEE Instrumentation Measurement Conf., Budapest, Hungary, 2001, pp. 1365-1369.
   

Wiener systems

1. •Bai, E.W., “A Blind Approach to Hammerstein-Wiener Model Identification”, Automatica, Vol. 38, 2002, pp. 967-979
   

2. •Bai, E.W., “Frequency Domain Identification of Wiener Models”, Automatica, Vol. 39, 2003, pp. 1521-1530.
   

3. •Bai EW and J Reyland, “Towards identification of Wiener systems with the least amount of a priori information on the nonlinearity”, Automatica, Vol. 44, pp.910-919, 2008
   

4. •Bai EW and J Reyland, “Towards identification of Wiener systems with the least amount of a priori information on the nonlinearity: IIR cases”, Automatica, Vol. 45, pp.956-965, 2009
   

Cell system identification

1. •Haxhinasto, K., A. Kamath, K. Blackwell, J. Bodmer, A.English, E.W. Bai and A. Moy, “l-Caldmon alters cytoskeletal-memberance function independent of myosin AToase and actin assembly in fibroblasts”, Am J. Physiol Cell Physiology, Vol. 287 C1125-C1138, 2004
   

2. •J. Bodmer, A. English, M. Brady, K. Blackwell, K. Haxinasto, S. Fotedar, K. Borgman, E.W. Bai, and A. Moy, “Modeling Error and Stability of Endothelial Cytoskeletal-Membrane Parameters Based on Modeling Transendothelial Impedance as Resistor and Capacitor in series”, AJP-Cell, Physiology, 289, C735-C747, May, 2005
   

3. •Er-Wei Bai, Sunaina Fotedar and Alan Moy, “Modeling and Parameter Estimation of a Cell System”, International Journal of Modeling, Identification and Control, Vol. 6, pp72-80, 2009
   

Muscle modeling

1. •Er-Wei Bai, Zhijun Cai, Shauna Dudley-Javorosk, Richard K. Shields, “Identification of a Modified Wiener-Hammerstein System and Its Application in Electrically Stimulated Paralyzed Skeletal Muscle Modeling”, Automatica,  Vol. 45, pp.736-743, 2009
   

2. •Zhijun Cai, Er-Wei Bai and Richard K. Shields, “Fatigue and Non-Fatigue Mathematical Muscle Models During Functional Electrical Stimulation of Paralyzed Muscle”, Journal of Biomedical Signal Processing and Control, Vol. 5, pp.87-93, 2010