Ellipsoidal parameter or state estimation under model uncertainty

Authors:
Boris T. Polyak;Sergey A. Nazin;CéCile Durieu;Eric Walter
Affiliations:
Institute of Control Sciences, Russian Academy of Sciences, 65 Profsojuznaja st., Moscow 117997, Russia;Institute of Control Sciences, Russian Academy of Sciences, 65 Profsojuznaja st., Moscow 117997, Russia;SATIE, CNRS-ENS de Cachan, 61 av. du Président Wilson, 94235 Cachan, France;Laboratoire des Signaux et Systemès, CNRS-Supélec-UPS, 91192 Gif-sur-Yvette, France
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.