Identification discrete fractional order Hammerstein systems

New algorithm is proposed for identification single-input-single-output (SISO) discrete fractional order Hammerstein systems. The estimates are proved to be convergent to the true values with probability one. The results of a simulated example indicate that the proposed algorithm provides good estimates.

[1]  A. Méhauté,et al.  Fractal Geometries Theory and Applications , 1991 .

[2]  D. Westwick,et al.  Identification of a Hammerstein model of the stretch reflex EMG using separable least squares , 2000, Proceedings of the 22nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (Cat. No.00CH37143).

[3]  Peter J. Torvik,et al.  FRACTIONAL CALCULUS - A DIFFERENT APPROACH TO THE FINITE ELEMENT ANALYSIS OF VISCOELASTICALLY DAMPED STRUCTURES. , 1981 .

[4]  Michael Stiassnie,et al.  On the application of fractional calculus for the formulation of viscoelastic models , 1979 .

[5]  Alain Oustaloup,et al.  The CRONE Control of Resonant Plants: Application to a Flexible Transmission , 1995, Eur. J. Control.

[6]  D. Ivanov,et al.  Identification discrete fractional order linear dynamic systems with output-error , 2013, 2013 International Siberian Conference on Control and Communications (SIBCON).

[7]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[8]  J. Sabatier,et al.  TUTORIAL ON SYSTEM IDENTIFICATION USING FRACTIONAL DIFFERENTIATION MODELS , 2006 .

[9]  D. Sierociuk,et al.  Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation , 2006 .

[10]  Zi-Qiang Lang,et al.  Controller design oriented model identification method for Hammerstein system, , 1993, Autom..

[11]  Igor Podlubny,et al.  Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation , 2001, math/0110241.

[12]  M. J. Kownberg Recent Advances In The Identification Of Nonlinear Systems: Minimum-variance Approximation By Hammerstein Models , 1991, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society Volume 13: 1991.

[13]  A. Oustaloup,et al.  Fractional state variable filter for system identification by fractional model , 2001, 2001 European Control Conference (ECC).

[14]  Steven C. Bass,et al.  Adaptive noise cancellation for a class of nonlinear, dynamic reference channels , 1985 .

[15]  M. Korenberg Identification of Nonlinear Systems , 1994 .

[16]  J. Machado Analysis and design of fractional-order digital control systems , 1997 .

[17]  V. Zaborovsky,et al.  Informational network traffic model based on fractional calculus , 2001, 2001 International Conferences on Info-Tech and Info-Net. Proceedings (Cat. No.01EX479).

[18]  Igor M. Sokolov,et al.  Physics of Fractal Operators , 2003 .

[19]  Alain Oustaloup,et al.  Non Integer Model from Modal Decomposition for Time Domain System Identification , 2000 .

[20]  Stanley H. Johnson,et al.  Use of Hammerstein Models in Identification of Nonlinear Systems , 1991 .

[21]  Alain Oustaloup,et al.  SYSTEM IDENTIFICATION USING FRACTIONAL HAMMERSTEIN MODELS , 2002 .

[22]  J. Martinez-vega,et al.  Application of fractional calculus to modelling of relaxation phenomena of organic dielectric materials , 2004, Proceedings of the 2004 IEEE International Conference on Solid Dielectrics, 2004. ICSD 2004..

[23]  D. V. Ivanov,et al.  Identification discrete fractional order linear dynamic systems with errors-in-variables , 2013, East-West Design & Test Symposium (EWDTS 2013).