A DIRECT APPROACH TO IDENTIFICATION OF NONLINEAR DIFFERENTIAL MODELS FROM DISCRETE DATA

Abstract The paper introduces a direct approach to the identification of non-linear differential equations from noisy input/output data. Both the parameter estimation and the structure determination problems are addressed. Central to the proposed methodology are two algorithms, a numerical differentiation algorithm involving fixed interval Kalman smoothing and an orthogonal regression routine used to perform model structure selection. The applicability of the identification procedure, which unlike most previous algorithms is not restricted to a special class of non-linear systems, is demonstrated using simulated and experimental noise corrupted data.

[1]  Daniel Coca,et al.  Continuous-Time System Identification for Linear and Nonlinear Systems Using Wavelet Decompositions , 1997 .

[2]  Peter C. Young,et al.  Data-Based Mechanistic Modeling of Engineering Systems , 1998 .

[3]  Peter C. Young,et al.  Recursive Estimation and Time Series Analysis , 1984 .

[4]  Michael Peter Kennedy,et al.  Three steps to chaos. II. A Chua's circuit primer , 1993 .

[5]  S. A. Billings,et al.  Reconstruction of linear and non-linear continuous time models from discrete time sampled-data systems , 1992 .

[6]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Stephen A. Billings,et al.  Direct parameter identification of distributed parameter systems , 2000, Int. J. Syst. Sci..

[8]  松本 隆,et al.  Bifurcations : sights, sounds, and mathematics , 1993 .

[9]  Sheng Chen,et al.  Extended model set, global data and threshold model identification of severely non-linear systems , 1989 .

[10]  Eric R. Ziegel,et al.  Developments in Time Series Analysis , 1993 .

[11]  J. Meditch.  A survey of data smoothing for linear and nonlinear dynamic systems , 1973 .

[12]  H. Unbehauen,et al.  Identification of continuous-time systems , 1991 .

[13]  Peter C. Young,et al.  Recursive estimation and forecasting of non‐stationary time series , 1990 .

[14]  Peter C. Young,et al.  A Direct Approach to the Identification and Estimation of Continuous-time Systems from Discrete-time Data Based on Fixed Interval Smoothing , 1993 .

[15]  L. Jetto,et al.  Accurate derivative estimation from noisy data: a state-space approach , 1989 .

[16]  H. Unbehauen,et al.  Identification of continuous systems , 1987 .

[17]  William A. Sethares,et al.  Smoothing of discontinuous signals: the competitive approach , 1995, IEEE Trans. Signal Process..

[18]  Anthony J. Jakeman,et al.  Joint parameter/state estimation , 1979 .

[19]  H. Dedieu,et al.  CONTROLLING CHAOS IN CHUA’S CIRCUIT VIA SAMPLED INPUTS , 1994 .

[20]  Peter Young,et al.  Parameter estimation for continuous-time models - A survey , 1979, Autom..

[21]  Sheng Chen,et al.  Representations of non-linear systems: the NARMAX model , 1989 .

[22]  Peter C. Young,et al.  Identification and system parameter estimation , 1985 .

[23]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[24]  H. Unbehauen,et al.  Identification of a class of nonlinear continuous-time systems using Hartley modulating functions , 1995 .

[25]  L. Chua.  The Genesis of Chua's circuit , 1992 .