Problems of quantile control and generalized confidence sets under conditions of incomplete information

Problems of optimal control containing random perturbations with incomplete information about their distribution are considered. The optimality criterion is the minimax quantile criterion. Such problems of quantile control are closely related to the problem of constructing confidence estimates for a random vector with an inexactly known distribution. The notion of a generalized confidence set is introduced, and the properties of such sets that are used for confidence estimation of random vectors in conditions of incomplete information are considered. A new approach to solving the problem of minimax quantile control is proposed. This approach is based on the optimal choice of the generalized confidence set.