CONSTRAINED ODE MODELING AND KALMAN FILTERING FOR RECURSIVE IDENTIFICATION OF NONLINEAR SYSTEMS

Abstract

A recursive identification algorithm for systems described by nonlinear ordinary differential equation (ODE) models is proposed. The ODE model is parameterized with coefficients of a polynomial in the state variables and inputs, that describes one component of the right hand side function of the ODE. This avoids over-parameterization problems. The model is then discretized with an Euler integration method. The algorithm exploits a Kalman filter, where the state variables needed in the right hand side function are derived by numerical differentiation. This approach makes a standard Kalman filter applicable to the identification problem. Contrary to a previously described RPEM algorithm, the proposed Kalman filter scheme cannot converge to false local minima of the criterion function. The proposed algorithm is therefore suitable for generation of initial values for the RPEM. The performance of the Kalman filter based algorithm is illustrated using a numerical example.