Recursive identification of Hammerstein systems with application to electrically stimulated muscle

Two methods for recursive identification of Hammerstein systems are considered. In the first method, the recursive least squares algorithm is applied to an overparameterized representation of the Hammerstein model and a rank-1 approximation is used to recover the linear and nonlinear parameters from the estimated overparameterized form. In the second method, the linear and nonlinear parameters are recursively estimated in an alternate manner. The superiority of the second method is confirmed using a numerical simulation example, together with experimentally measured data from electrically stimulated muscles.

[1]  M. Munih,et al.  Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle , 1998, IEEE Transactions on Biomedical Engineering.

[2]  K. Narendra,et al.  An iterative method for the identification of nonlinear systems using a Hammerstein model , 1966 .

[3]  Er-Wei Bai,et al.  A blind approach to the Hammerstein-Wiener model identification , 2002, Autom..

[4]  M. Boutayeb,et al.  Recursive identification method for MISO Wiener-Hammerstein model , 1995, IEEE Trans. Autom. Control..

[5]  Ning Lan.  Stability analysis for postural control in a two-joint limb system , 2002, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[6]  Jörg Raisch,et al.  Online identification and nonlinear control of the electrically stimulated quadriceps muscle , 2005 .

[7]  R Riener,et al.  Patient-driven control of FES-supported standing up: a simulation study. , 1998, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[8]  Ann-Marie Hughes,et al.  A model of the upper extremity using FES for stroke rehabilitation. , 2009, Journal of biomechanical engineering.

[9]  R. Riener,et al.  Model-based control of FES-induced single joint movements , 2001, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[10]  H.J. Chizeck,et al.  Robust closed-loop control of isometric muscle force using pulsewidth modulation , 1988, IEEE Transactions on Biomedical Engineering.

[11]  D. Westwick,et al.  Separable Least Squares Identification of Nonlinear Hammerstein Models: Application to Stretch Reflex Dynamics , 2001, Annals of Biomedical Engineering.

[12]  Eric Rogers,et al.  An upper limb model using FES for stroke rehabilitation , 2009, 2009 European Control Conference (ECC).

[13]  P. Crago,et al.  Nonlinear joint angle control for artificially stimulated muscle , 1992, IEEE Transactions on Biomedical Engineering.

[14]  Wen-Xiao Zhao,et al.  Adaptive tracking and recursive identification for Hammerstein systems , 2009, Autom..

[15]  Er-Wei Bai.  An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998, Autom..

[16]  Thierry Keller,et al.  Sliding mode closed-loop control of FES controlling the shank movement , 2004, IEEE Transactions on Biomedical Engineering.

[17]  Maarten J. IJzerman,et al.  Relation between stimulation characteristics and clinical outcome in studies using electrical stimulation to improve motor control of the upper extremity in stroke. , 2005, Journal of rehabilitation medicine.

[18]  Han-Fu Chen,et al.  Pathwise convergence of recursive identification algorithms for Hammerstein systems , 2004, IEEE Transactions on Automatic Control.

[19]  R Happee,et al.  The control of shoulder muscles during goal directed movements, an inverse dynamic analysis. , 1992, Journal of biomechanics.

[20]  W. Durfee,et al.  Estimation of force-activation, force-length, and force-velocity properties in isolated, electrically stimulated muscle , 1994, IEEE Transactions on Biomedical Engineering.

[21]  R. Luus,et al.  A noniterative method for identification using Hammerstein model , 1971 .

[22]  D. Lake.  Neuromuscular Electrical Stimulation , 1992, Sports medicine.

[23]  L. A. Bernotas,et al.  A Discrete-Time Model of Electrcally Stimulated Muscle , 1986, IEEE Transactions on Biomedical Engineering.

[24]  H.J. Chizeck,et al.  Recursive parameter identification of constrained systems: an application to electrically stimulated muscle , 1991, IEEE Transactions on Biomedical Engineering.

[25]  Mohamed Darouach,et al.  A robust and recursive identification method for MISO Hammerstein model , 1996 .

[26]  M. Popovic,et al.  The effect of random modulation of functional electrical stimulation parameters on muscle fatigue , 2006, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[27]  A. Hill.  The heat of shortening and the dynamic constants of muscle , 1938 .

[28]  Er-Wei Bai,et al.  Decoupling the linear and nonlinear parts in Hammerstein model identification , 2004, Autom..

[29]  M. Solomonow,et al.  The dynamic response model of nine different skeletal muscles , 1990, IEEE Transactions on Biomedical Engineering.

[30]  Zhijun Cai,et al.  Fatigue and non-fatigue mathematical muscle models during functional electrical stimulation of paralyzed muscle , 2010, Biomed. Signal Process. Control..

[31]  Wlodzimierz Greblicki,et al.  Stochastic approximation in nonparametric identification of Hammerstein systems , 2002, IEEE Trans. Autom. Control..

[32]  Han-Fu Chen,et al.  Identification and Stochastic Adaptive Control , 1991 .

[33]  David T. Westwick,et al.  Identification of Hammerstein models with cubic spline nonlinearities , 2004, IEEE Transactions on Biomedical Engineering.

[34]  Eric Rogers,et al.  Identification of electrically stimulated muscle models of stroke patients , 2010 .

[35]  Yucai Zhu.  Identification of Hammerstein models for control using ASYM , 2000 .

[36]  P H Chappell,et al.  A robotic workstation for stroke rehabilitation of the upper extremity using FES. , 2009, Medical engineering & physics.

[37]  M. Munih,et al.  Setup and procedure for online identification of electrically stimulated muscle with Matlab Simulink , 2001, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[38]  E. Bai.  An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998 .

[39]  Emanuele Carpanzano,et al.  Design of a gain scheduling controller for knee-joint angle control by using functional electrical stimulation , 2003, IEEE Trans. Control. Syst. Technol..

[40]  Er-Wei Bai,et al.  Identification of a modified Wiener-Hammerstein system and its application in electrically stimulated paralyzed skeletal muscle modeling , 2009, Autom..

[41]  Stéphane Lecoeuche,et al.  Recursive subspace identification of Hammerstein models based on least squares support vector machines , 2009 .

[42]  E. Rogers,et al.  Feasibility of Iterative Learning Control Mediated by Functional Electrical Stimulation for Reaching After Stroke , 2009, Neurorehabilitation and neural repair.

[43]  W. Durfee,et al.  Methods for estimating isometric recruitment curves of electrically stimulated muscle , 1989, IEEE Transactions on Biomedical Engineering.

[44]  J. Quintern,et al.  A physiologically based model of muscle activation verified by electrical stimulation , 1997 .

[45]  Timothy D. Lee,et al.  Motor Control and Learning: A Behavioral Emphasis , 1982 .