A Direct Approach to Identification of Nonlinear Differential Models from Discrete Data

The paper introduces a direct approach to the identification of nonlinear 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. Thw applicability of the identification procedure, which unlike most previous algorithms, is not restricted to a special class of nonlinear systems, is demonstrated using simulated and experimental noise corrupted data.