Control under indeterminacy and double constraints (Q1776218)

A class of uncertain linear control systems is considered. It is assumed that the control is constrained both geometrically and integrally, while the noise is subjected only to a geometrical constraint. The considered problem is to find the solvability set and a positional control strategy such that all admissible trajectories, starting from a point of the solvability set, reach a suitably defined objective set at the terminal time. This problem is solved using some constructions of the Krasovskii extremal aiming as well as the Pontryagin alternating integral. The same problem is also studied for an appropriate class of positional controls without the integral constraint.