External Ellipsoidal Estimation of the Union of Two Concentric Ellipsoids and Its Applications

For an arbitrary set representable as the convex hull formed by the union of two concentric ellipsoids we propose a method to construct a family of external undominated ellipsoidal approximations and represent the estimated set as the intersection of all estimates from a given family. A sufficient condition of undominated guaranteed ellipsoidal approximation of a convex compactum is derived. A method is described that for certain classes of sets (such as the intersection of an ellipsoid or a cone with two halfspaces) constructs a family of internal undominated ellipsoidal approximations using the previous formulas for the external estimates of the union of concentric ellipsoids.