Optimal strategies in a pursuit problem with incomplete information

One of the variants of control problem investigation with incomplete information about phase vector is connected with transition to state description as point sets in the phase space (so called information sets) compatible with information about system behaviour accumulated to the given moment. The problem is formulated as a control problem of the information set change in time to minimize different indices. Since information set depends on a current reading the minimax statements arise naturally where the first player manages useful control and the second player runs reading choice. A model pursuit problem with incomplete information is considered. The case is studied when information sets are segments. There are proved optimality of the suggested strategies of feedback and given the modeling results.