Asymptotic Attainability

The effect of an unstability can arise in extremal problems or in other related problems. In this connection, we note the known problem of constructing the attainability domain in con­ trol theory. This text deals with the construction of correct extensions of extremal problems including problems of multicriterial optimization and more general problems of optimization with respect to a cone. The methods of qualitative stability and asymptotically insensitive analysis proposed here are particularly applicable to problems of optimal control with integrally constrained openloop controls. A non-traditional mathematical tool using elements of finitely-additive measure theory is applied, which necessitated special research concerned with approximative analogues of the Radon-Nikodym property. These abstract constructions do, however, address the essence of the problem at hand, and may find other applications as well.