Comparing different approaches to model error modeling in robust identification

Abstract

Identification for robust control must deliver not only a nominal model, but also a reliable estimate of the uncertainty associated with the model. This paper addresses recent approaches to robust identification, that aim at dealing with contributions from the two main uncertainty sources: unmodeled dynamics and noise affecting the data. In particular, the following methods are considered: non-stationary Stochastic Embedding, Model Error Modeling based on prediction error methods and Set Membership Identification. Moreover, we show how Set Membership Identification can be embedded into a Model Error Modeling framework. Model validation issues are easily addressed in the proposed framework. It is shown how the computation of the minimum noise bound for which a nominal model is not falsified by input-output data, can be used as a rationale for selecting an appropriate model class in the set membership setting. For all three methods, uncertainty is evaluated in terms of the frequency response, so that it can be handled by H ∞ control techniques. An example, where a nontrivial undermodeling is ensured by the presence of a nonlinearity in the system generating the data, is presented to compare the different methods.

From experiment design to closed-loop control

“…Interestingly, it seems as if many of these different approaches result in similar unfalsified model sets, see Reinelt, Garulli, and Ljung (2002).…”

Towards Robustness in Neural Network Based Fault Diagnosis

“…This usually leads to least squares estimation and prediction error methods. Model Error Modelling (MEM) employs prediction error methods to identify a model from input-output data (Reinelt et al, 2002). After that, one can estimate the uncertainty of the model by analyzing residuals evaluated from the inputs.…”

On-Line Sensor Monitoring in an Active Front Steering System Using Extended Kalman Filtering

“…prediction error methods, see [5] or unknown-but-bounded approaches, including parameter validation on validation data and a final assessment of the parameter quality. An overview and comparison of recent methods is given by [8].…”