Ellipsoidal Techniques: Control Synthesis for Uncertain Systems

Kurzhanski, A.B. & Valyi, I. (1991). Ellipsoidal Techniques: Control Synthesis for Uncertain Systems. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-91-007

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Abstract

This paper deals with a technique of solving the problem of control synthesis under unknown but bounded disturbances that allows an algrithmization with an appropriate graphic simulation. The original theoretical solution scheme taken here comes from the theory introduced by N.N. Krasovski, from the notion of the "alternated integral" of L.S. Pontriagin and the "funnel equation" in the form given by Kurzhanski and Nikonov. The theory is used as a point of application of constructive schemes generated through ellipsoidal techniques developed by the authors. A concise exposition of the latter is the objective of this paper. A particular feature is that the ellipsoidal techniques introduced here do indicate an exact approximation of the original solutions based on set-valued calculus by solutions formulated in terms of ellipsoidal valued functions only.

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