LEAST-SQUARE IDENTIFICATION WITH ERROR-BOUNDS FOR REAL-TIME SIGNAL-PROCESSING AND CONTROL

This paper is concerned with set-membership (SM) identification that refers to a class of algorithms that uses certain a priori knowledge about a parametric model to constrain the solutions to certain sets. The emerging field of SM-based system identification for signal processing and control is receiving increasing international attention. This paper focuses on a class of SM-based techniques that are of particular interest in applications requiring real-time processing. The optimal bounding ellipsoid (OBE) algorithms are interpreted as a blending of the classical least-square error minimization approach, with knowledge of bounds on model errors arising from SM considerations. Using this interpretation, a general framework embracing all currently used OBE algorithms is developed, then strategies for adaptation and for implementation on parallel machines are discussed. Computational complexity benefits are considered for the various algorithms. The paper is tutorial, leaving many of the formal details to an appendix that presents an archival theoretical treatment of the key results. This appendix serves to unify many related results appearing in the literature. A second appendix gives an overview of current research in the general SM identification field.