The problem of control synthesis for uncertain systems: ellipsoidal techniques

This paper deals with a constructive technique of solving the problem of control synthesis under unknown but bounded disturbances in such a way 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 [1], from the notion of the “alternated integral” of L. S. Pontriagin [2] and the “funnel equation” in the form given in [3]. 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 approximati on of the original solutions based on set-valued calculus by solutions formulated in terms of ellipsoidal valued functions only