MODEL VALIDATION FOR ROBUST CONTROL AND CONTROLLER VALIDATION IN A PREDICTION ERROR FRAMEWORK Michel Gevers ∗ , Xavier Bombois ∗ , Benoˆ ıt Codrons ∗ , Franky De Bruyne ∗∗ and G´ erard Scorletti ∗∗∗ ∗ CESAME, Universit´ e Catholique de Louvain Bˆatiment EULER, 4 av. Georges Lemaitre, B-1348 Louvain-la-Neuve, Belgium E-mail: Gevers@csam.ucl.ac.be ∗∗ Siemens,Service EIT ES5, Demeurslaan 132, Building 15/0+, B-1654 Huizingen, Belgium E-mail: Franky.De-Bruyne@Siemens.be ∗∗∗ LAP ISMRA,6 boulevard du Mar´ echal Juin, F-14050 Caen Cedex, France Email: gerard.scorletti@greyc.ismra.fr Abstract: 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. Copyright c  2000 IFAC Keywords: identification, validation, robust stability, robust performance 1. INTRODUCTION This paper presents in summary form the key ideas and results that we have developed over the last few years on model validation for con- trol and controller validation, in the prediction error identification framework. The full presenta- tion of these results, as well as the proofs, can be found in the comprehensive paper (Gevers et al., 2000), and in the more technical support- ing papers (Gevers et al., 1999a), (Bombois et 1 The authors acknowledge the Belgian Programme on Inter-university Poles of Attraction, initiated by the Bel- gian State, Prime Minister’s Office for Science, Technology and Culture. The scientific responsibility rests with its authors. al., 1999b), (Bombois et al., 1999c), (Gevers et al., 1999b), (Bombois et al., 1999a), (Bombois et al., 2000b), (Bombois et al., 2000a). Our results on validation establish a robust stability and robust performance theory for model uncertainty sets produced by prediction error identification and validation, which we call PE uncertainty sets for ease of reference. In the case of full order models, these validated PE model uncertainty sets are de- fined by parametrized transfer function sets whose parameter vectors lie in ellipsoids in parameter space. In the case of restricted complexity models, they are obtained by a stochastic embedding tech- nique (see (Goodwin et al., 1992)) and are made up of ellipsoids at every frequency in the space of transfer functions (Bombois et al., 2000a). These