Recursive Prediction Error Identification and Scaling of Non-linear Systems with Midpoint Numerical Integration

A new recursive prediction error algorithm (RPEM) based on a non-linear ordinary differential equation (ODE) model of black-box state space form is presented. The selected model is discretised by a midpoint integration algorithm and compared to an Euler forward algorithm. When the algorithm is applied, scaling of the sampling time is used to improve performance further. This affects the state vector, the parameter vector and the Hessian. This impact is analysed and described in three Theorems. Numerical examples are provided to verify the theoretical results obtained.