Recursive Prediction Error Identification of Nonlinear State Space Models

A recursive prediction error algorithm for identification of systems described by nonlinear ordinary differential equation (ODE) models is presented. The model is a MIMO ODE model, parameterized with coefficients of a multi-variable polynomial that describes one component of the right hand side function of the ODE. It is explained why such a parameterization is a key to obtain a well defined algorithm, that does not suffer from singularities and over-parameterization problems. Furthermore, it is proved that the selected model can also handle systems with more complicated right hand side structure, by identification of an input-output equivalent system in the coordinate system of the selected states. The linear output measurements can be corrupted by zero mean disturbances that are correlated between measurements and over time. The disturbance correlation matrix is estimated online and need not be known beforehand. The algorithm is applied to live data from a system consisting of two cascaded tanks with free outlets. It is illustrated that the identification algorithm is capable of producing a highly accurate nonlinear model of the system, despite the fact that the right hand structure of the system has two nontrivial nonlinear components. A novel technique based on scaling of the sampling period that significantly improves the numerical properties of the algorithm is also disclosed.