Ellipsoidal techniques for dynamic systems: Control synthesis for uncertain systems

This article is a continuation of the work reported in [4], introducing unknown but bounded disturbances into the problem of control synthesis studied there. The technique presented allows an algorithmization 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]. For alternative treatment of related problems, see also [5], [6], and [7]. 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 article. 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.