Ellipsoidal Techniques: Guaranteed State Estimation

Kurzhanski, A.B. & Valyi, I. (1991). Ellipsoidal Techniques: Guaranteed State Estimation. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-91-021

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Abstract

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.

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