Model validation for robust control and controller validation in a prediction error framework

This paper presents a coherent framework for model validation for control and for controller validation (for stability and for performance) in the context where the validated model uncertainty sets are obtained by prediction error identification methods. Thus, these uncertainty sets are parametrized transfer function sets, with parameters lying in ellipsoidal regions in parameter space. Our results cover two distinct aspects: (1) Control-oriented model validation results, where we show that a measure of size of the validated model set is connected to the size of the model-based controller set that robustly stabilizes the model set, leading to validation design guidelines. (2) Controller validation results, where we present necessary and sufficient conditions for a controller to stabilize all models, or to achieve a given level of performance for all models, in such uncertainty set.