Ellipsoidal Techniques: Guaranteed State Estimation

This paper gives a concise description of effective solutions to the "guaranteed" state estimation problems for dynamic systems with unknown but bounded uncertainty. It indicates a rather unconventional, rigorous theory for these problems based on the notion of evolution equations of the "funnel" type which could be further transformed -- through exact ellipsoidal approximations -- into algorithmic procedures that allow effective simulation particularly with computer graphics. The estimation problem is also interpreted as a problem of tracking a partially known system under incomplete measurements. Mathematically, the technique described in this paper is based on a theory of set-valued evolution equations with the approximation of solutions formulated in terms of set-valued calculus by ellipsoidal-valued functions