Simulation error minimization identification based on multi-stage prediction

Classical prediction error minimization (PEM) methods are widely used for model identification, but they are also known to provide satisfactory results only in specific identification conditions, e.g. disturbance model matching. If these conditions are not met, the obtained model may have quite different dynamical behavior compared with the original system, resulting in poor long range prediction or simulation performance, which is a critical factor for model analysis, simulation, model-based control design. In the mentioned non-ideal conditions a robust and reliable alternative is based on the minimization of the simulation error. Unfortunately, direct optimization of a simulation error minimization (SEM) criterion is an intrinsically complex and computationally intensive task. In this paper a low-complexity approximate SEM approach is discussed, based on the iteration of multi-step PEM methods. The soundness of the proposed approach is demonstrated by showing that, for sufficiently high prediction horizons, the k-steps ahead (single- or multi-step) PEM criteria converge to the SEM one. Identifiability issues and convergence properties of the algorithm are also discussed. Some examples are provided to illustrate the mentioned properties of the algorithm.