Convergence analysis and experiments using an RPEM based on nonlinear ODEs and midpoint integration

A convergence analysis is performed for a recursive prediction error algorithm based on nonlinear ODEs and the midpoint integration algorithm. Several conditions are formulated such that the stability of an associated differential equation can be tied to the local and global convergence properties of the algorithm. This is used to show that the algorithm converges to a minimum point of the criterion function, which may or may not be unique. A consequence is that convergence to the true parameters is possible. As compared to previous work, complete system assumptions are integrated in the analysis, thereby generalising previous results. The theoretical analysis of this paper is complemented with numerical examples and with live data experiments.